CVXPY: A Python-Embedded Modeling Language for Convex Optimization

PubMed Central

Diamond, Steven; Boyd, Stephen

2016-01-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples. PMID:27375369

Reentry trajectory optimization with waypoint and no-fly zone constraints using multiphase convex programming

NASA Astrophysics Data System (ADS)

Zhao, Dang-Jun; Song, Zheng-Yu

2017-08-01

This study proposes a multiphase convex programming approach for rapid reentry trajectory generation that satisfies path, waypoint and no-fly zone (NFZ) constraints on Common Aerial Vehicles (CAVs). Because the time when the vehicle reaches the waypoint is unknown, the trajectory of the vehicle is divided into several phases according to the prescribed waypoints, rendering a multiphase optimization problem with free final time. Due to the requirement of rapidity, the minimum flight time of each phase index is preferred over other indices in this research. The sequential linearization is used to approximate the nonlinear dynamics of the vehicle as well as the nonlinear concave path constraints on the heat rate, dynamic pressure, and normal load; meanwhile, the convexification techniques are proposed to relax the concave constraints on control variables. Next, the original multiphase optimization problem is reformulated as a standard second-order convex programming problem. Theoretical analysis is conducted to show that the original problem and the converted problem have the same solution. Numerical results are presented to demonstrate that the proposed approach is efficient and effective.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azunre, P.

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore » of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.« less

Medial-based deformable models in nonconvex shape-spaces for medical image segmentation.

PubMed

McIntosh, Chris; Hamarneh, Ghassan

2012-01-01

We explore the application of genetic algorithms (GA) to deformable models through the proposition of a novel method for medical image segmentation that combines GA with nonconvex, localized, medial-based shape statistics. We replace the more typical gradient descent optimizer used in deformable models with GA, and the convex, implicit, global shape statistics with nonconvex, explicit, localized ones. Specifically, we propose GA to reduce typical deformable model weaknesses pertaining to model initialization, pose estimation and local minima, through the simultaneous evolution of a large number of models. Furthermore, we constrain the evolution, and thus reduce the size of the search-space, by using statistically-based deformable models whose deformations are intuitive (stretch, bulge, bend) and are driven in terms of localized principal modes of variation, instead of modes of variation across the entire shape that often fail to capture localized shape changes. Although GA are not guaranteed to achieve the global optima, our method compares favorably to the prevalent optimization techniques, convex/nonconvex gradient-based optimizers and to globally optimal graph-theoretic combinatorial optimization techniques, when applied to the task of corpus callosum segmentation in 50 mid-sagittal brain magnetic resonance images.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skala, Vaclav

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E{sup 2} a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E{sup 3} case, the complexity is O(N) even for the convex polyhedron as no orderingmore » is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.« less

Mathematical Optimization Techniques

NASA Technical Reports Server (NTRS)

Bellman, R. (Editor)

1963-01-01

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.

ɛ-subgradient algorithms for bilevel convex optimization

NASA Astrophysics Data System (ADS)

Helou, Elias S.; Simões, Lucas E. A.

2017-05-01

This paper introduces and studies the convergence properties of a new class of explicit ɛ-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. ES Helou was supported by FAPESP grants 2013/07375-0 and 2013/16508-3 and CNPq grant 311476/2014-7. LEA Simões was supported by FAPESP grants 2011/02219-4 and 2013/14615-7.

Convex Accelerated Maximum Entropy Reconstruction

PubMed Central

Worley, Bradley

2016-01-01

Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. PMID:26894476

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

PubMed

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

2013-01-01

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Statistical estimation via convex optimization for trending and performance monitoring

NASA Astrophysics Data System (ADS)

Samar, Sikandar

This thesis presents an optimization-based statistical estimation approach to find unknown trends in noisy data. A Bayesian framework is used to explicitly take into account prior information about the trends via trend models and constraints. The main focus is on convex formulation of the Bayesian estimation problem, which allows efficient computation of (globally) optimal estimates. There are two main parts of this thesis. The first part formulates trend estimation in systems described by known detailed models as a convex optimization problem. Statistically optimal estimates are then obtained by maximizing a concave log-likelihood function subject to convex constraints. We consider the problem of increasing problem dimension as more measurements become available, and introduce a moving horizon framework to enable recursive estimation of the unknown trend by solving a fixed size convex optimization problem at each horizon. We also present a distributed estimation framework, based on the dual decomposition method, for a system formed by a network of complex sensors with local (convex) estimation. Two specific applications of the convex optimization-based Bayesian estimation approach are described in the second part of the thesis. Batch estimation for parametric diagnostics in a flight control simulation of a space launch vehicle is shown to detect incipient fault trends despite the natural masking properties of feedback in the guidance and control loops. Moving horizon approach is used to estimate time varying fault parameters in a detailed nonlinear simulation model of an unmanned aerial vehicle. An excellent performance is demonstrated in the presence of winds and turbulence.

Fractional Programming for Communication Systems—Part I: Power Control and Beamforming

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic transform technique for tackling the multiple-ratio concave-convex FP problem--in contrast to conventional FP techniques that mostly can only deal with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are important for the optimization of communication networks, because system-level design often involves multiple signal-to-interference-plus-noise ratio terms. This paper considers the applications of FP to solving continuous problems in communication system design, particularly for power control, beamforming, and energy efficiency maximization. These application cases illustrate that the proposed quadratic transform can greatly facilitate the optimization involving ratios by recasting the original nonconvex problem as a sequence of convex problems. This FP-based problem reformulation gives rise to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper further demonstrates close connections between the proposed FP approach and other well-known algorithms in the literature, such as the fixed-point iteration and the weighted minimum mean-square-error beamforming. The optimization of discrete problems is discussed in Part II of this paper.

Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity

NASA Astrophysics Data System (ADS)

Briec, Walter; Horvath, Charles

2008-05-01

-convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103-127]. Separation and Hahn-Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237-257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13-30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., volE 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696-729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity.

Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging

NASA Astrophysics Data System (ADS)

Repetti, Audrey; Birdi, Jasleen; Dabbech, Arwa; Wiaux, Yves

2017-10-01

Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as clean. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the Square Kilometre Array, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, I.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. matlab code is available on GitHub.

A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks

PubMed Central

Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian

2013-01-01

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ℓ0 minimization problem. Then, we relax this non-convex optimization to a convex ℓ1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms. PMID:23989826

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

DOE PAGES

Azunre, P.

2016-09-21

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore » of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.« less

Energy Efficiency Maximization for WSNs with Simultaneous Wireless Information and Power Transfer

PubMed Central

Yu, Hongyan; Zhang, Yongqiang; Yang, Yuanyuan; Ji, Luyue

2017-01-01

Recently, the simultaneous wireless information and power transfer (SWIPT) technique has been regarded as a promising approach to enhance performance of wireless sensor networks with limited energy supply. However, from a green communication perspective, energy efficiency optimization for SWIPT system design has not been investigated in Wireless Rechargeable Sensor Networks (WRSNs). In this paper, we consider the tradeoffs between energy efficiency and three factors including spectral efficiency, the transmit power and outage target rate for two different modes, i.e., power splitting (PS) and time switching modes (TS), at the receiver. Moreover, we formulate the energy efficiency maximization problem subject to the constraints of minimum Quality of Service (QoS), minimum harvested energy and maximum transmission power as non-convex optimization problem. In particular, we focus on optimizing power control and power allocation policy in PS and TS modes to maximize energy efficiency of data transmission. For PS and TS modes, we propose the corresponding algorithm to characterize a non-convex optimization problem that takes into account the circuit power consumption and the harvested energy. By exploiting nonlinear fractional programming and Lagrangian dual decomposition, we propose suboptimal iterative algorithms to obtain the solutions of non-convex optimization problems. Furthermore, we derive the outage probability and effective throughput from the scenarios that the transmitter does not or partially know the channel state information (CSI) of the receiver. Simulation results illustrate that the proposed optimal iterative algorithm can achieve optimal solutions within a small number of iterations and various tradeoffs between energy efficiency and spectral efficiency, transmit power and outage target rate, respectively. PMID:28820496

Energy Efficiency Maximization for WSNs with Simultaneous Wireless Information and Power Transfer.

PubMed

Yu, Hongyan; Zhang, Yongqiang; Guo, Songtao; Yang, Yuanyuan; Ji, Luyue

2017-08-18

Recently, the simultaneous wireless information and power transfer (SWIPT) technique has been regarded as a promising approach to enhance performance of wireless sensor networks with limited energy supply. However, from a green communication perspective, energy efficiency optimization for SWIPT system design has not been investigated in Wireless Rechargeable Sensor Networks (WRSNs). In this paper, we consider the tradeoffs between energy efficiency and three factors including spectral efficiency, the transmit power and outage target rate for two different modes, i.e., power splitting (PS) and time switching modes (TS), at the receiver. Moreover, we formulate the energy efficiency maximization problem subject to the constraints of minimum Quality of Service (QoS), minimum harvested energy and maximum transmission power as non-convex optimization problem. In particular, we focus on optimizing power control and power allocation policy in PS and TS modes to maximize energy efficiency of data transmission. For PS and TS modes, we propose the corresponding algorithm to characterize a non-convex optimization problem that takes into account the circuit power consumption and the harvested energy. By exploiting nonlinear fractional programming and Lagrangian dual decomposition, we propose suboptimal iterative algorithms to obtain the solutions of non-convex optimization problems. Furthermore, we derive the outage probability and effective throughput from the scenarios that the transmitter does not or partially know the channel state information (CSI) of the receiver. Simulation results illustrate that the proposed optimal iterative algorithm can achieve optimal solutions within a small number of iterations and various tradeoffs between energy efficiency and spectral efficiency, transmit power and outage target rate, respectively.

Computational Efficiency of the Simplex Embedding Method in Convex Nondifferentiable Optimization

NASA Astrophysics Data System (ADS)

Kolosnitsyn, A. V.

2018-02-01

The simplex embedding method for solving convex nondifferentiable optimization problems is considered. A description of modifications of this method based on a shift of the cutting plane intended for cutting off the maximum number of simplex vertices is given. These modification speed up the problem solution. A numerical comparison of the efficiency of the proposed modifications based on the numerical solution of benchmark convex nondifferentiable optimization problems is presented.

Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

NASA Astrophysics Data System (ADS)

Rosenberg, D. E.; Alafifi, A.

2016-12-01

Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one step to any point in the near-optimal region, and each iterate generates a new, feasible alternative. We use the method to generate alternatives that span the near-optimal regions of simple and more complicated water management problems and may be preferred to optimal solutions. We also discuss extensions to handle non-linear equity constraints.

Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.

PubMed

Craft, David

2010-10-01

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. Copyright © 2009 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Distance majorization and its applications.

PubMed

Chi, Eric C; Zhou, Hua; Lange, Kenneth

2014-08-01

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.

Nonconvex Sparse Logistic Regression With Weakly Convex Regularization

NASA Astrophysics Data System (ADS)

Shen, Xinyue; Gu, Yuantao

2018-06-01

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a method based on proximal gradient descent is used to solve the general weakly convex sparse logistic regression, and its convergence behavior is studied theoretically. Then the general framework is applied to a specific weakly convex function, and a necessary and sufficient local optimality condition is provided. The solution method is instantiated in this case as an iterative firm-shrinkage algorithm, and its effectiveness is demonstrated in numerical experiments by both randomly generated and real datasets.

Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms.

PubMed

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2015-12-01

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we use our new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild!) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algorithms for non-convex matrix problems including matrix completion; and (3) we design and analyze an asynchronous SGD algorithm, called Buckwild!, that uses lower-precision arithmetic. We show experimentally that our algorithms run efficiently for a variety of problems on modern hardware.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

Directional Convexity and Finite Optimality Conditions.

DTIC Science & Technology

1984-03-01

system, Necessary Conditions for optimality. Work Unit Number 5 (Optimization and Large Scale Systems) *Istituto di Matematica Applicata, Universita...that R(T) is convex would then imply x(u,T) e int R(T). Cletituto di Matematica Applicata, Universita di Padova, 35100 ITALY. Sponsored by the United

Block clustering based on difference of convex functions (DC) programming and DC algorithms.

PubMed

Le, Hoai Minh; Le Thi, Hoai An; Dinh, Tao Pham; Huynh, Van Ngai

2013-10-01

We investigate difference of convex functions (DC) programming and the DC algorithm (DCA) to solve the block clustering problem in the continuous framework, which traditionally requires solving a hard combinatorial optimization problem. DC reformulation techniques and exact penalty in DC programming are developed to build an appropriate equivalent DC program of the block clustering problem. They lead to an elegant and explicit DCA scheme for the resulting DC program. Computational experiments show the robustness and efficiency of the proposed algorithm and its superiority over standard algorithms such as two-mode K-means, two-mode fuzzy clustering, and block classification EM.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xiaohu; Shi, Di; Wang, Zhiwei

Shunt FACTS devices, such as, a Static Var Compensator (SVC), are capable of providing local reactive power compensation. They are widely used in the network to reduce the real power loss and improve the voltage profile. This paper proposes a planning model based on mixed integer conic programming (MICP) to optimally allocate SVCs in the transmission network considering load uncertainty. The load uncertainties are represented by a number of scenarios. Reformulation and linearization techniques are utilized to transform the original non-convex model into a convex second order cone programming (SOCP) model. Numerical case studies based on the IEEE 30-bus systemmore » demonstrate the effectiveness of the proposed planning model.« less

Distance majorization and its applications

PubMed Central

Chi, Eric C.; Zhou, Hua; Lange, Kenneth

2014-01-01

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton’s method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications. PMID:25392563

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

A robust optimization methodology for preliminary aircraft design

NASA Astrophysics Data System (ADS)

Prigent, S.; Maréchal, P.; Rondepierre, A.; Druot, T.; Belleville, M.

2016-05-01

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

First-order convex feasibility algorithms for x-ray CT

PubMed Central

Sidky, Emil Y.; Jørgensen, Jakob S.; Pan, Xiaochuan

2013-01-01

Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution—thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle−Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application. PMID:23464295

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination.

PubMed

Khoo, Y; Singer, A; Cowburn, D

2017-07-01

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms-RDC-SOS and RDC-NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

Virtual sensors for active noise control in acoustic-structural coupled enclosures using structural sensing: robust virtual sensor design.

PubMed

Halim, Dunant; Cheng, Li; Su, Zhongqing

2011-03-01

The work was aimed to develop a robust virtual sensing design methodology for sensing and active control applications of vibro-acoustic systems. The proposed virtual sensor was designed to estimate a broadband acoustic interior sound pressure using structural sensors, with robustness against certain dynamic uncertainties occurring in an acoustic-structural coupled enclosure. A convex combination of Kalman sub-filters was used during the design, accommodating different sets of perturbed dynamic model of the vibro-acoustic enclosure. A minimax optimization problem was set up to determine an optimal convex combination of Kalman sub-filters, ensuring an optimal worst-case virtual sensing performance. The virtual sensing and active noise control performance was numerically investigated on a rectangular panel-cavity system. It was demonstrated that the proposed virtual sensor could accurately estimate the interior sound pressure, particularly the one dominated by cavity-controlled modes, by using a structural sensor. With such a virtual sensing technique, effective active noise control performance was also obtained even for the worst-case dynamics. © 2011 Acoustical Society of America

Multi-Stage Convex Relaxation Methods for Machine Learning

DTIC Science & Technology

2013-03-01

Many problems in machine learning can be naturally formulated as non-convex optimization problems. However, such direct nonconvex formulations have...original nonconvex formulation. We will develop theoretical properties of this method and algorithmic consequences. Related convex and nonconvex machine learning methods will also be investigated.

Random search optimization based on genetic algorithm and discriminant function

NASA Technical Reports Server (NTRS)

Kiciman, M. O.; Akgul, M.; Erarslanoglu, G.

1990-01-01

The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.

Generalized Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1983-04-11

existing ones. * -37- !I T-472 REFERENCES [1] Avriel, M., W. E. Diewert, S. Schaible and W. T. Ziemba (1981). Introduction to concave and generalized concave...functions. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba , eds.), Academic Press, New York, pp. 21-50. (21 Bank...Optimality conditions involving generalized convex mappings. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba

Linear Controller Design: Limits of Performance

DTIC Science & Technology

1991-01-01

where a sensor should be placed eg where an accelerometer is to be positioned on an aircraft or where a strain gauge is placed along a beam The...309 VIII CONTENTS 14 Special Algorithms for Convex Optimization 311 Notation and Problem Denitions...311 On Algorithms for Convex Optimization 312 CuttingPlane Algorithms

Algorithms for Mathematical Programming with Emphasis on Bi-level Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldfarb, Donald; Iyengar, Garud

2014-05-22

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

WE-AB-209-07: Explicit and Convex Optimization of Plan Quality Metrics in Intensity-Modulated Radiation Therapy Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Engberg, L; KTH Royal Institute of Technology, Stockholm; Eriksson, K

Purpose: To formulate objective functions of a multicriteria fluence map optimization model that correlate well with plan quality metrics, and to solve this multicriteria model by convex approximation. Methods: In this study, objectives of a multicriteria model are formulated to explicitly either minimize or maximize a dose-at-volume measure. Given the widespread agreement that dose-at-volume levels play important roles in plan quality assessment, these objectives correlate well with plan quality metrics. This is in contrast to the conventional objectives, which are to maximize clinical goal achievement by relating to deviations from given dose-at-volume thresholds: while balancing the new objectives means explicitlymore » balancing dose-at-volume levels, balancing the conventional objectives effectively means balancing deviations. Constituted by the inherently non-convex dose-at-volume measure, the new objectives are approximated by the convex mean-tail-dose measure (CVaR measure), yielding a convex approximation of the multicriteria model. Results: Advantages of using the convex approximation are investigated through juxtaposition with the conventional objectives in a computational study of two patient cases. Clinical goals of each case respectively point out three ROI dose-at-volume measures to be considered for plan quality assessment. This is translated in the convex approximation into minimizing three mean-tail-dose measures. Evaluations of the three ROI dose-at-volume measures on Pareto optimal plans are used to represent plan quality of the Pareto sets. Besides providing increased accuracy in terms of feasibility of solutions, the convex approximation generates Pareto sets with overall improved plan quality. In one case, the Pareto set generated by the convex approximation entirely dominates that generated with the conventional objectives. Conclusion: The initial computational study indicates that the convex approximation outperforms the conventional objectives in aspects of accuracy and plan quality.« less

Identification of optimal feedback control rules from micro-quadrotor and insect flight trajectories.

PubMed

Faruque, Imraan A; Muijres, Florian T; Macfarlane, Kenneth M; Kehlenbeck, Andrew; Humbert, J Sean

2018-06-01

This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

Scalable Rapidly Deployable Convex Optimization for Data Analytics

DTIC Science & Technology

SOCPs , SDPs, exponential cone programs, and power cone programs. CVXPY supports basic methods for distributed optimization, on...multiple heterogenous platforms. We have also done basic research in various application areas , using CVXPY , to demonstrate its usefulness. See attached report for publication information....Over the period of the contract we have developed the full stack for wide use of convex optimization, in machine learning and many other areas .

Piecewise convexity of artificial neural networks.

PubMed

Rister, Blaine; Rubin, Daniel L

2017-10-01

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. First, that the network is piecewise convex as a function of the input data. Second, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Third, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize the objective on certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space. Copyright © 2017 Elsevier Ltd. All rights reserved.

Optimal boundary regularity for a singular Monge-Ampère equation

NASA Astrophysics Data System (ADS)

Jian, Huaiyu; Li, You

2018-06-01

In this paper we study the optimal global regularity for a singular Monge-Ampère type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity of the domain. We introduce (a , η) type to describe the convexity. As a result, we show that the more convex is the domain, the better is the regularity of the solution. In particular, the regularity is the best near angular points.

Graph Matching: Relax at Your Own Risk.

PubMed

Lyzinski, Vince; Fishkind, Donniell E; Fiori, Marcelo; Vogelstein, Joshua T; Priebe, Carey E; Sapiro, Guillermo

2016-01-01

Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Fast globally optimal segmentation of 3D prostate MRI with axial symmetry prior.

PubMed

Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron

2013-01-01

We propose a novel global optimization approach to segmenting a given 3D prostate T2w magnetic resonance (MR) image, which enforces the inherent axial symmetry of the prostate shape and simultaneously performs a sequence of 2D axial slice-wise segmentations with a global 3D coherence prior. We show that the proposed challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. With this regard, we introduce a novel coupled continuous max-flow model, which is dual to the studied convex relaxed optimization formulation and leads to an efficient multiplier augmented algorithm based on the modern convex optimization theory. Moreover, the new continuous max-flow based algorithm was implemented on GPUs to achieve a substantial improvement in computation. Experimental results using public and in-house datasets demonstrate great advantages of the proposed method in terms of both accuracy and efficiency.

Geometric convex cone volume analysis

NASA Astrophysics Data System (ADS)

Li, Hsiao-Chi; Chang, Chein-I.

2016-05-01

Convexity is a major concept used to design and develop endmember finding algorithms (EFAs). For abundance unconstrained techniques, Pixel Purity Index (PPI) and Automatic Target Generation Process (ATGP) which use Orthogonal Projection (OP) as a criterion, are commonly used method. For abundance partially constrained techniques, Convex Cone Analysis is generally preferred which makes use of convex cones to impose Abundance Non-negativity Constraint (ANC). For abundance fully constrained N-FINDR and Simplex Growing Algorithm (SGA) are most popular methods which use simplex volume as a criterion to impose ANC and Abundance Sum-to-one Constraint (ASC). This paper analyze an issue encountered in volume calculation with a hyperplane introduced to illustrate an idea of bounded convex cone. Geometric Convex Cone Volume Analysis (GCCVA) projects the boundary vectors of a convex cone orthogonally on a hyperplane to reduce the effect of background signatures and a geometric volume approach is applied to address the issue arose from calculating volume and further improve the performance of convex cone-based EFAs.

Comparative analysis of Pareto surfaces in multi-criteria IMRT planning

NASA Astrophysics Data System (ADS)

Teichert, K.; Süss, P.; Serna, J. I.; Monz, M.; Küfer, K. H.; Thieke, C.

2011-06-01

In the multi-criteria optimization approach to IMRT planning, a given dose distribution is evaluated by a number of convex objective functions that measure tumor coverage and sparing of the different organs at risk. Within this context optimizing the intensity profiles for any fixed set of beams yields a convex Pareto set in the objective space. However, if the number of beam directions and irradiation angles are included as free parameters in the formulation of the optimization problem, the resulting Pareto set becomes more intricate. In this work, a method is presented that allows for the comparison of two convex Pareto sets emerging from two distinct beam configuration choices. For the two competing beam settings, the non-dominated and the dominated points of the corresponding Pareto sets are identified and the distance between the two sets in the objective space is calculated and subsequently plotted. The obtained information enables the planner to decide if, for a given compromise, the current beam setup is optimal. He may then re-adjust his choice accordingly during navigation. The method is applied to an artificial case and two clinical head neck cases. In all cases no configuration is dominating its competitor over the whole Pareto set. For example, in one of the head neck cases a seven-beam configuration turns out to be superior to a nine-beam configuration if the highest priority is the sparing of the spinal cord. The presented method of comparing Pareto sets is not restricted to comparing different beam angle configurations, but will allow for more comprehensive comparisons of competing treatment techniques (e.g. photons versus protons) than with the classical method of comparing single treatment plans.

Numerical Optimization of converging diverging miniature cavitating nozzles

NASA Astrophysics Data System (ADS)

Chavan, Kanchan; Bhingole, B.; Raut, J.; Pandit, A. B.

2015-12-01

The work focuses on the numerical optimization of converging diverging cavitating nozzles through nozzle dimensions and wall shape. The objective is to develop design rules for the geometry of cavitating nozzles for desired end-use. Two main aspects of nozzle design which affects the cavitation have been studied i.e. end dimensions of the geometry (i.e. angle and/or curvature of the inlet, outlet and the throat and the lengths of the converging and diverging sections) and wall curvatures(concave or convex). Angle of convergence at the inlet was found to control the cavity growth whereas angle of divergence of the exit controls the collapse of cavity. CFD simulations were carried out for the straight line converging and diverging sections by varying converging and diverging angles to study its effect on the collapse pressure generated by the cavity. Optimized geometry configurations were obtained on the basis of maximum Cavitational Efficacy Ratio (CER)i.e. cavity collapse pressure generated for a given permanent pressure drop across the system. With increasing capabilities in machining and fabrication, it is possible to exploit the effect of wall curvature to create nozzles with further increase in the CER. Effect of wall curvature has been studied for the straight, concave and convex shapes. Curvature has been varied and effect of concave and convex wall curvatures vis-à-vis straight walls studied for fixed converging and diverging angles.It is concluded that concave converging-diverging nozzles with converging angle of 20° and diverging angle of 5° with the radius of curvature 0.03 m and 0.1530 m respectively gives maximum CER. Preliminary experiments using optimized geometry are indicating similar trends and are currently being carried out. Refinements of the CFD technique using two phase flow simulations are planned.

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage.

PubMed

Aggarwal, Priya; Shrivastava, Parth; Kabra, Tanay; Gupta, Anubha

2017-03-01

This paper presents a new accelerated fMRI reconstruction method, namely, OptShrink LR + S method that reconstructs undersampled fMRI data using a linear combination of low-rank and sparse components. The low-rank component has been estimated using non-convex optimal singular value shrinkage algorithm, while the sparse component has been estimated using convex l 1 minimization. The performance of the proposed method is compared with the existing state-of-the-art algorithms on real fMRI dataset. The proposed OptShrink LR + S method yields good qualitative and quantitative results.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

An optimal algorithm for reconstructing images from binary measurements

NASA Astrophysics Data System (ADS)

Yang, Feng; Lu, Yue M.; Sbaiz, Luciano; Vetterli, Martin

2010-01-01

We have studied a camera with a very large number of binary pixels referred to as the gigavision camera [1] or the gigapixel digital film camera [2, 3]. Potential advantages of this new camera design include improved dynamic range, thanks to its logarithmic sensor response curve, and reduced exposure time in low light conditions, due to its highly sensitive photon detection mechanism. We use maximum likelihood estimator (MLE) to reconstruct a high quality conventional image from the binary sensor measurements of the gigavision camera. We prove that when the threshold T is "1", the negative loglikelihood function is a convex function. Therefore, optimal solution can be achieved using convex optimization. Base on filter bank techniques, fast algorithms are given for computing the gradient and the multiplication of a vector and Hessian matrix of the negative log-likelihood function. We show that with a minor change, our algorithm also works for estimating conventional images from multiple binary images. Numerical experiments with synthetic 1-D signals and images verify the effectiveness and quality of the proposed algorithm. Experimental results also show that estimation performance can be improved by increasing the oversampling factor or the number of binary images.

Optimization of Wireless Power Transfer Systems Enhanced by Passive Elements and Metasurfaces

NASA Astrophysics Data System (ADS)

Lang, Hans-Dieter; Sarris, Costas D.

2017-10-01

This paper presents a rigorous optimization technique for wireless power transfer (WPT) systems enhanced by passive elements, ranging from simple reflectors and intermedi- ate relays all the way to general electromagnetic guiding and focusing structures, such as metasurfaces and metamaterials. At its core is a convex semidefinite relaxation formulation of the otherwise nonconvex optimization problem, of which tightness and optimality can be confirmed by a simple test of its solutions. The resulting method is rigorous, versatile, and general -- it does not rely on any assumptions. As shown in various examples, it is able to efficiently and reliably optimize such WPT systems in order to find their physical limitations on performance, optimal operating parameters and inspect their working principles, even for a large number of active transmitters and passive elements.

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

PubMed Central

Sidky, Emil Y.; Jørgensen, Jakob H.; Pan, Xiaochuan

2012-01-01

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented. PMID:22538474

Convex relaxations for gas expansion planning

DOE PAGES

Borraz-Sanchez, Conrado; Bent, Russell Whitford; Backhaus, Scott N.; ...

2016-01-01

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutionsmore » to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution« less

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Convex Formulations of Learning from Crowds

NASA Astrophysics Data System (ADS)

Kajino, Hiroshi; Kashima, Hisashi

It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in non-convex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.

Study on feed forward neural network convex optimization for LiFePO4 battery parameters

NASA Astrophysics Data System (ADS)

Liu, Xuepeng; Zhao, Dongmei

2017-08-01

Based on the modern facility agriculture automatic walking equipment LiFePO4 Battery, the parameter identification of LiFePO4 Battery is analyzed. An improved method for the process model of li battery is proposed, and the on-line estimation algorithm is presented. The parameters of the battery are identified using feed forward network neural convex optimization algorithm.

Powered Descent Guidance with General Thrust-Pointing Constraints

NASA Technical Reports Server (NTRS)

Carson, John M., III; Acikmese, Behcet; Blackmore, Lars

2013-01-01

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Joint terminals and relay optimization for two-way power line information exchange systems with QoS constraints

NASA Astrophysics Data System (ADS)

Wu, Xiaolin; Rong, Yue

2015-12-01

The quality-of-service (QoS) criteria (measured in terms of the minimum capacity requirement in this paper) are very important to practical indoor power line communication (PLC) applications as they greatly affect the user experience. With a two-way multicarrier relay configuration, in this paper we investigate the joint terminals and relay power optimization for the indoor broadband PLC environment, where the relay node works in the amplify-and-forward (AF) mode. As the QoS-constrained power allocation problem is highly non-convex, the globally optimal solution is computationally intractable to obtain. To overcome this challenge, we propose an alternating optimization (AO) method to decompose this problem into three convex/quasi-convex sub-problems. Simulation results demonstrate the fast convergence of the proposed algorithm under practical PLC channel conditions. Compared with the conventional bidirectional direct transmission (BDT) system, the relay-assisted two-way information exchange (R2WX) scheme can meet the same QoS requirement with less total power consumption.

Compensation of modal dispersion in multimode fiber systems using adaptive optics via convex optimization

NASA Astrophysics Data System (ADS)

Panicker, Rahul Alex

Multimode fibers (MMF) are widely deployed in local-, campus-, and storage-area-networks. Achievable data rates and transmission distances are, however, limited by the phenomenon of modal dispersion. We propose a system to compensate for modal dispersion using adaptive optics. This leads to a 10- to 100-fold improvement in performance over current standards. We propose a provably optimal technique for minimizing inter-symbol interference (ISI) in MMF systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes. Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity. Simulations show that this technique opens up an eye pattern originally closed due to ISI. We then propose fast, low-complexity adaptive algorithms for optimizing the SLM settings. We show that some of these converge to the global optimum in the absence of noise. We also propose modified versions of these algorithms to improve resilience to noise and speed of convergence. Next, we experimentally compare the proposed adaptive algorithms in 50-mum graded-index (GRIN) MMFs using a liquid-crystal SLM. We show that continuous-phase sequential coordinate ascent (CPSCA) gives better bit-error-ratio performance than 2- or 4-phase sequential coordinate ascent, in concordance with simulations. We evaluate the bandwidth characteristics of CPSCA, and show that a single SLM is able to simultaneously compensate over up to 9 wavelength-division-multiplexed (WDM) 10-Gb/s channels, spaced by 50 GHz, over a total bandwidth of 450 GHz. We also show that CPSCA is able to compensate for modal dispersion over up to 2.2 km, even in the presence of mid-span connector offsets up to 4 mum (simulated in experiment by offset splices). A known non-adaptive launching technique using a fusion-spliced single-mode-to-multimode patchcord is shown to fail under these conditions. Finally, we demonstrate 10 x 10 Gb/s dense WDM transmission over 2.2 km of 50-mum GRIN MMF. We combine transmitter-based adaptive optics and receiver-based single-mode filtering, and control the launched field pattern for ten 10-Gb/s non-return-to-zero channels, wavelength-division multiplexed on a 200-GHz grid in the C band. We achieve error-free transmission through 2.2 km of 50-mum GRIN MMF for launch offsets up to 10 mum and for worst-case launched polarization. We employ a ten-channel transceiver based on parallel integration of electronics and photonics.

Poster — Thur Eve — 69: Computational Study of DVH-guided Cancer Treatment Planning Optimization Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghomi, Pooyan Shirvani; Zinchenko, Yuriy

2014-08-15

Purpose: To compare methods to incorporate the Dose Volume Histogram (DVH) curves into the treatment planning optimization. Method: The performance of three methods, namely, the conventional Mixed Integer Programming (MIP) model, a convex moment-based constrained optimization approach, and an unconstrained convex moment-based penalty approach, is compared using anonymized data of a prostate cancer patient. Three plans we generated using the corresponding optimization models. Four Organs at Risk (OARs) and one Tumor were involved in the treatment planning. The OARs and Tumor were discretized into total of 50,221 voxels. The number of beamlets was 943. We used commercially available optimization softwaremore » Gurobi and Matlab to solve the models. Plan comparison was done by recording the model runtime followed by visual inspection of the resulting dose volume histograms. Conclusion: We demonstrate the effectiveness of the moment-based approaches to replicate the set of prescribed DVH curves. The unconstrained convex moment-based penalty approach is concluded to have the greatest potential to reduce the computational effort and holds a promise of substantial computational speed up.« less

A One-Layer Recurrent Neural Network for Real-Time Portfolio Optimization With Probability Criterion.

PubMed

Liu, Qingshan; Dang, Chuangyin; Huang, Tingwen

2013-02-01

This paper presents a decision-making model described by a recurrent neural network for dynamic portfolio optimization. The portfolio-optimization problem is first converted into a constrained fractional programming problem. Since the objective function in the programming problem is not convex, the traditional optimization techniques are no longer applicable for solving this problem. Fortunately, the objective function in the fractional programming is pseudoconvex on the feasible region. It leads to a one-layer recurrent neural network modeled by means of a discontinuous dynamic system. To ensure the optimal solutions for portfolio optimization, the convergence of the proposed neural network is analyzed and proved. In fact, the neural network guarantees to get the optimal solutions for portfolio-investment advice if some mild conditions are satisfied. A numerical example with simulation results substantiates the effectiveness and illustrates the characteristics of the proposed neural network.

Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2015-01-01

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2015-01-01

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

Scalable splitting algorithms for big-data interferometric imaging in the SKA era

NASA Astrophysics Data System (ADS)

Onose, Alexandru; Carrillo, Rafael E.; Repetti, Audrey; McEwen, Jason D.; Thiran, Jean-Philippe; Pesquet, Jean-Christophe; Wiaux, Yves

2016-11-01

In the context of next-generation radio telescopes, like the Square Kilometre Array (SKA), the efficient processing of large-scale data sets is extremely important. Convex optimization tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimization algorithmic structures able to solve the convex optimization tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iterations and can be seen, by analogy, with the CLEAN major-minor cycle, as running sophisticated CLEAN-like iterations in parallel in multiple data, prior, and image spaces. Both methods support any convex regularization function, in particular, the well-studied ℓ1 priors promoting image sparsity in an adequate domain. Tailored for big-data, they employ parallel and distributed computations to achieve scalability, in terms of memory and computational requirements. One of them also exploits randomization, over data blocks at each iteration, offering further flexibility. We present simulation results showing the feasibility of the proposed methods as well as their advantages compared to state-of-the-art algorithmic solvers. Our MATLAB code is available online on GitHub.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

PubMed

Daducci, Alessandro; Canales-Rodríguez, Erick J; Zhang, Hui; Dyrby, Tim B; Alexander, Daniel C; Thiran, Jean-Philippe

2015-01-15

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

A Convex Formulation for Magnetic Particle Imaging X-Space Reconstruction.

PubMed

Konkle, Justin J; Goodwill, Patrick W; Hensley, Daniel W; Orendorff, Ryan D; Lustig, Michael; Conolly, Steven M

2015-01-01

Magnetic Particle Imaging (mpi) is an emerging imaging modality with exceptional promise for clinical applications in rapid angiography, cell therapy tracking, cancer imaging, and inflammation imaging. Recent publications have demonstrated quantitative mpi across rat sized fields of view with x-space reconstruction methods. Critical to any medical imaging technology is the reliability and accuracy of image reconstruction. Because the average value of the mpi signal is lost during direct-feedthrough signal filtering, mpi reconstruction algorithms must recover this zero-frequency value. Prior x-space mpi recovery techniques were limited to 1d approaches which could introduce artifacts when reconstructing a 3d image. In this paper, we formulate x-space reconstruction as a 3d convex optimization problem and apply robust a priori knowledge of image smoothness and non-negativity to reduce non-physical banding and haze artifacts. We conclude with a discussion of the powerful extensibility of the presented formulation for future applications.

Localized Multiple Kernel Learning A Convex Approach

DTIC Science & Technology

2016-11-22

data. All the aforementioned approaches to localized MKL are formulated in terms of non-convex optimization problems, and deep the- oretical...learning. IEEE Transactions on Neural Networks, 22(3):433–446, 2011. Jingjing Yang, Yuanning Li, Yonghong Tian, Lingyu Duan, and Wen Gao. Group-sensitive

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process

PubMed Central

Yuen, Kam Chuen; Shen, Ying

2015-01-01

We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655

Development and Application of Optimization Techniques for Composite Laminates.

DTIC Science & Technology

1983-09-01

Institute of Technolgy Air University in Partial Fulfillment of the Requirements for the Degree of Master of Science by Gerald V. Flanagan, S.B. Lt. USAF...global minima [9]. An informal definition of convexity is that any two points in the space can be connected by a straight line which does not pass out of...question. A quick look at gradient information suggests that too few angles (2 for example) will make the laminate sensitive to small changes in

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron

2008-01-01

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

A Depth-Adjustment Deployment Algorithm Based on Two-Dimensional Convex Hull and Spanning Tree for Underwater Wireless Sensor Networks.

PubMed

Jiang, Peng; Liu, Shuai; Liu, Jun; Wu, Feng; Zhang, Le

2016-07-14

Most of the existing node depth-adjustment deployment algorithms for underwater wireless sensor networks (UWSNs) just consider how to optimize network coverage and connectivity rate. However, these literatures don't discuss full network connectivity, while optimization of network energy efficiency and network reliability are vital topics for UWSN deployment. Therefore, in this study, a depth-adjustment deployment algorithm based on two-dimensional (2D) convex hull and spanning tree (NDACS) for UWSNs is proposed. First, the proposed algorithm uses the geometric characteristics of a 2D convex hull and empty circle to find the optimal location of a sleep node and activate it, minimizes the network coverage overlaps of the 2D plane, and then increases the coverage rate until the first layer coverage threshold is reached. Second, the sink node acts as a root node of all active nodes on the 2D convex hull and then forms a small spanning tree gradually. Finally, the depth-adjustment strategy based on time marker is used to achieve the three-dimensional overall network deployment. Compared with existing depth-adjustment deployment algorithms, the simulation results show that the NDACS algorithm can maintain full network connectivity with high network coverage rate, as well as improved network average node degree, thus increasing network reliability.

A Depth-Adjustment Deployment Algorithm Based on Two-Dimensional Convex Hull and Spanning Tree for Underwater Wireless Sensor Networks

PubMed Central

Jiang, Peng; Liu, Shuai; Liu, Jun; Wu, Feng; Zhang, Le

2016-01-01

Most of the existing node depth-adjustment deployment algorithms for underwater wireless sensor networks (UWSNs) just consider how to optimize network coverage and connectivity rate. However, these literatures don’t discuss full network connectivity, while optimization of network energy efficiency and network reliability are vital topics for UWSN deployment. Therefore, in this study, a depth-adjustment deployment algorithm based on two-dimensional (2D) convex hull and spanning tree (NDACS) for UWSNs is proposed. First, the proposed algorithm uses the geometric characteristics of a 2D convex hull and empty circle to find the optimal location of a sleep node and activate it, minimizes the network coverage overlaps of the 2D plane, and then increases the coverage rate until the first layer coverage threshold is reached. Second, the sink node acts as a root node of all active nodes on the 2D convex hull and then forms a small spanning tree gradually. Finally, the depth-adjustment strategy based on time marker is used to achieve the three-dimensional overall network deployment. Compared with existing depth-adjustment deployment algorithms, the simulation results show that the NDACS algorithm can maintain full network connectivity with high network coverage rate, as well as improved network average node degree, thus increasing network reliability. PMID:27428970

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

PubMed

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

NASA Astrophysics Data System (ADS)

Gaddy, Melissa R.; Yıldız, Sercan; Unkelbach, Jan; Papp, Dávid

2018-01-01

Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on five cases with distinct geometries. The computed spatiotemporal plans achieve 12-35% mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97% of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.

A Bayesian observer replicates convexity context effects in figure-ground perception.

PubMed

Goldreich, Daniel; Peterson, Mary A

2012-01-01

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.

Formulation of image fusion as a constrained least squares optimization problem

PubMed Central

Dwork, Nicholas; Lasry, Eric M.; Pauly, John M.; Balbás, Jorge

2017-01-01

Abstract. Fusing a lower resolution color image with a higher resolution monochrome image is a common practice in medical imaging. By incorporating spatial context and/or improving the signal-to-noise ratio, it provides clinicians with a single frame of the most complete information for diagnosis. In this paper, image fusion is formulated as a convex optimization problem that avoids image decomposition and permits operations at the pixel level. This results in a highly efficient and embarrassingly parallelizable algorithm based on widely available robust and simple numerical methods that realizes the fused image as the global minimizer of the convex optimization problem. PMID:28331885

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

Computationally efficient stochastic optimization using multiple realizations

NASA Astrophysics Data System (ADS)

Bayer, P.; Bürger, C. M.; Finkel, M.

2008-02-01

The presented study is concerned with computationally efficient methods for solving stochastic optimization problems involving multiple equally probable realizations of uncertain parameters. A new and straightforward technique is introduced that is based on dynamically ordering the stack of realizations during the search procedure. The rationale is that a small number of critical realizations govern the output of a reliability-based objective function. By utilizing a problem, which is typical to designing a water supply well field, several variants of this "stack ordering" approach are tested. The results are statistically assessed, in terms of optimality and nominal reliability. This study demonstrates that the simple ordering of a given number of 500 realizations while applying an evolutionary search algorithm can save about half of the model runs without compromising the optimization procedure. More advanced variants of stack ordering can, if properly configured, save up to more than 97% of the computational effort that would be required if the entire number of realizations were considered. The findings herein are promising for similar problems of water management and reliability-based design in general, and particularly for non-convex problems that require heuristic search techniques.

A distributed approach to the OPF problem

NASA Astrophysics Data System (ADS)

Erseghe, Tomaso

2015-12-01

This paper presents a distributed approach to optimal power flow (OPF) in an electrical network, suitable for application in a future smart grid scenario where access to resource and control is decentralized. The non-convex OPF problem is solved by an augmented Lagrangian method, similar to the widely known ADMM algorithm, with the key distinction that penalty parameters are constantly increased. A (weak) assumption on local solver reliability is required to always ensure convergence. A certificate of convergence to a local optimum is available in the case of bounded penalty parameters. For moderate sized networks (up to 300 nodes, and even in the presence of a severe partition of the network), the approach guarantees a performance very close to the optimum, with an appreciably fast convergence speed. The generality of the approach makes it applicable to any (convex or non-convex) distributed optimization problem in networked form. In the comparison with the literature, mostly focused on convex SDP approximations, the chosen approach guarantees adherence to the reference problem, and it also requires a smaller local computational complexity effort.

L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing

NASA Astrophysics Data System (ADS)

Demetriou, I. C.

2006-04-01

Fortran 77 software is given for least squares smoothing to data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is also unknown of the optimization problem. A highly useful description of the constraints is that they follow from the assumption of initially increasing and subsequently decreasing rates of change, or vice versa, of the process considered. The underlying algorithm partitions the data into two disjoint sets of adjacent data and calculates the required fit by solving a strictly convex quadratic programming problem for each set. The piecewise linear interpolant to the fit is convex on the first set and concave on the other one. The partition into suitable sets is achieved by a finite iterative algorithm, which is made quite efficient because of the interactions of the quadratic programming problems on consecutive data. The algorithm obtains the solution by employing no more quadratic programming calculations over subranges of data than twice the number of the divided differences constraints. The quadratic programming technique makes use of active sets and takes advantage of a B-spline representation of the smoothed values that allows some efficient updating procedures. The entire code required to implement the method is 2920 Fortran lines. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes over subranges of data that is only proportional to the number of data. The results suggest that the package can be used for very large numbers of data values. Some examples with output are provided to help new users and exhibit certain features of the software. Important applications of the smoothing technique may be found in calculating a sigmoid approximation, which is a common topic in various contexts in applications in disciplines like physics, economics, biology and engineering. Distribution material that includes single and double precision versions of the code, driver programs, technical details of the implementation of the software package and test examples that demonstrate the use of the software is available in an accompanying ASCII file. Program summaryTitle of program:L2CXCV Catalogue identifier:ADXM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXM_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:PC Intel Pentium, Sun Sparc Ultra 5, Hewlett-Packard HP UX 11.0 Operating system:WINDOWS 98, 2000, Unix/Solaris 7, Unix/HP UX 11.0 Programming language used:FORTRAN 77 Memory required to execute with typical data:O(n), where n is the number of data No. of bits in a byte:8 No. of lines in distributed program, including test data, etc.:29 349 No. of bytes in distributed program, including test data, etc.:1 276 663 No. of processors used:1 Has the code been vectorized or parallelized?:no Distribution format:default tar.gz Separate documentation available:Yes Nature of physical problem:Analysis of processes that show initially increasing and then decreasing rates of change (sigmoid shape), as, for example, in heat curves, reactor stability conditions, evolution curves, photoemission yields, growth models, utility functions, etc. Identifying an unknown convex/concave (sigmoid) function from some measurements of its values that contain random errors. Also, identifying the inflection point of this sigmoid function. Method of solution:Univariate data smoothing by minimizing the sum of the squares of the residuals (least squares approximation) subject to the condition that the second order divided differences of the smoothed values change sign at most once. Ideally, this is the number of sign changes in the second derivative of the underlying function. The remarkable property of the smoothed values is that they consist of one separate section of optimal components that give nonnegative second divided differences (convexity) and one separate section of optimal components that give nonpositive second divided differences (concavity). The solution process finds the joint (that is the inflection point estimate of the underlying function) of the sections automatically. The underlying method is iterative, each iteration solving a structured strictly convex quadratic programming problem in order to obtain a convex or a concave section over a subrange of data. Restrictions on the complexity of the problem:Number of data, n, is not limited in the software package, but is limited to 2000 in the main driver. The total work of the method requires 2n-2 structured quadratic programming calculations over subranges of data, which in practice does not exceed the amount of O(n) computer operations. Typical running times:CPU time on a PC with an Intel 733 MHz processor operating in Windows 98: About 2 s to smooth n=1000 noisy measurements that follow the shape of the sine function over one period. Summary:L2CXCV is a package of Fortran 77 subroutines for least squares smoothing to n univariate data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is unknown. The piecewise linear interpolant to the smoothed values gives a convex/concave fit to the data. The underlying algorithm is based on the property that in this best convex/concave fit, the convex and the concave section are both optimal and separate. The algorithm is iterative, each iteration solving a strictly convex quadratic programming problem for the best convex fit to the first k data, starting from the best convex fit to the first k-1 data. By reversing the order and sign of the data, the algorithm obtains the best concave fit to the last n-k data. Then it chooses that k as the optimal position of the required sign change (which defines the inflection point of the fit), if the convex and the concave components to the first k and the last n-k data, respectively, form a convex/concave vector that gives the least sum of squares of residuals. In effect the algorithm requires at most 2n-2 quadratic programming calculations over subranges of data. The package employs a technique for quadratic programming, which takes advantage of a B-spline representation of the smoothed values and makes use of some efficient O(k) updating procedures, where k is the number of data of a subrange. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes that is about n, thus exhibiting quadratic performance in n. The Fortran codes have been designed to minimize the use of computing resources. Attention has been given to computer rounding errors details, which are essential to the robustness of the software package. Numerical examples with output are provided to help the use of the software and exhibit certain features of the method. Distribution material that includes driver programs, technical details of the installation of the package and test examples that demonstrate the use of the software is available in an ASCII file that accompanies this work.

Optical performance of random anti-reflection structured surfaces (rARSS) on spherical lenses

NASA Astrophysics Data System (ADS)

Taylor, Courtney D.

Random anti-reflection structured surfaces (rARSS) have been reported to improve transmittance of optical-grade fused silica planar substrates to values greater than 99%. These textures are fabricated directly on the substrates using reactive-ion/inductively-coupled plasma etching (RIE/ICP) techniques, and often result in transmitted spectra with no measurable interference effects (fringes) for a wide range of wavelengths. The RIE/ICP processes used in the fabrication process to etch the rARSS is anisotropic and thus well suited for planar components. The improvement in spectral transmission has been found to be independent of optical incidence angles for values from 0° to +/-30°. Qualifying and quantifying the rARSS performance on curved substrates, such as convex lenses, is required to optimize the fabrication of the desired AR effect on optical-power elements. In this work, rARSS was fabricated on fused silica plano-convex (PCX) and plano-concave (PCV) lenses using a planar-substrate optimized RIE process to maximize optical transmission in the range from 500 to 1100 nm. An additional set of lenses were etched in a non-optimized ICP process to provide additional comparisons. Results are presented from optical transmission and beam propagation tests (optimized lenses only) of rARSS lenses for both TE and TM incident polarizations at a wavelength of 633 nm and over a 70° full field of view in both singlet and doublet configurations. These results suggest optimization of the fabrication process is not required, mainly due to the wide angle-of-incidence AR tolerance performance of the rARSS lenses. Non-optimized recipe lenses showed low transmission enhancement, and confirmed the need to optimized etch recipes prior to process transfer of PCX/PCV lenses. Beam propagation tests indicated no major beam degradation through the optimized lens elements. Scanning electron microscopy (SEM) images confirmed different structure between optimized and non-optimized samples. SEM images also indicated isotropically-oriented surface structures on both types of lenses.

Asteroid shape and spin statistics from convex models

NASA Astrophysics Data System (ADS)

Torppa, J.; Hentunen, V.-P.; Pääkkönen, P.; Kehusmaa, P.; Muinonen, K.

2008-11-01

We introduce techniques for characterizing convex shape models of asteroids with a small number of parameters, and apply these techniques to a set of 87 models from convex inversion. We present three different approaches for determining the overall dimensions of an asteroid. With the first technique, we measured the dimensions of the shapes in the direction of the rotation axis and in the equatorial plane and with the two other techniques, we derived the best-fit ellipsoid. We also computed the inertia matrix of the model shape to test how well it represents the target asteroid, i.e., to find indications of possible non-convex features or albedo variegation, which the convex shape model cannot reproduce. We used shape models for 87 asteroids to perform statistical analyses and to study dependencies between shape and rotation period, size, and taxonomic type. We detected correlations, but more data are required, especially on small and large objects, as well as slow and fast rotators, to reach a more thorough understanding about the dependencies. Results show, e.g., that convex models of asteroids are not that far from ellipsoids in root-mean-square sense, even though clearly irregular features are present. We also present new spin and shape solutions for Asteroids (31) Euphrosyne, (54) Alexandra, (79) Eurynome, (93) Minerva, (130) Elektra, (376) Geometria, (471) Papagena, and (776) Berbericia. We used a so-called semi-statistical approach to obtain a set of possible spin state solutions. The number of solutions depends on the abundancy of the data, which for Eurynome, Elektra, and Geometria was extensive enough for determining an unambiguous spin and shape solution. Data of Euphrosyne, on the other hand, provided a wide distribution of possible spin solutions, whereas the rest of the targets have two or three possible solutions.

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

A free gingival impression for achieving optimal interdental papilla height: a case report.

PubMed

Nozawa, Takeshi; Kitami, Norikazu; Tsurumaki, Shunzo; Enomoto, Hiroaki; Ito, Koichi

2011-02-01

Failure to tend to inadequate crown contours in the crown trial can cause long-term disharmony of the free gingival form. This case report describes a novel technique for free gingival impression from a final provisional restoration to a zirconia crown. Two die casts were manufactured from a silicone impression. The first die cast was for the zirconia crown; the second die cast was for the final provisional restoration and the provisionalized transfer coping. A free gingival impression was taken using a provisionalized transfer coping, and a soft gingival model was manufactured. The proximal contact position was managed using the predicted convex curve of the interdental papillae. One year after zirconia crown placement, no inflammation was observed around the pyramidal interdental papillae, and symmetric interdental papilla heights were evident. A free gingival impression using a two die-cast technique appears to be useful for achieving optimal interdental papilla height.

General and mechanistic optimal relationships for tensile strength of doubly convex tablets under diametrical compression.

PubMed

Razavi, Sonia M; Gonzalez, Marcial; Cuitiño, Alberto M

2015-04-30

We propose a general framework for determining optimal relationships for tensile strength of doubly convex tablets under diametrical compression. This approach is based on the observation that tensile strength is directly proportional to the breaking force and inversely proportional to a non-linear function of geometric parameters and materials properties. This generalization reduces to the analytical expression commonly used for flat faced tablets, i.e., Hertz solution, and to the empirical relationship currently used in the pharmaceutical industry for convex-faced tablets, i.e., Pitt's equation. Under proper parametrization, optimal tensile strength relationship can be determined from experimental results by minimizing a figure of merit of choice. This optimization is performed under the first-order approximation that a flat faced tablet and a doubly curved tablet have the same tensile strength if they have the same relative density and are made of the same powder, under equivalent manufacturing conditions. Furthermore, we provide a set of recommendations and best practices for assessing the performance of optimal tensile strength relationships in general. Based on these guidelines, we identify two new models, namely the general and mechanistic models, which are effective and predictive alternatives to the tensile strength relationship currently used in the pharmaceutical industry. Copyright © 2015 Elsevier B.V. All rights reserved.

Posterior convex release and interbody fusion for thoracic scoliosis: technical note.

PubMed

Mac-Thiong, Jean-Marc; Asghar, Jahangir; Parent, Stefan; Shufflebarger, Harry L; Samdani, Amer; Labelle, Hubert

2016-09-01

Anterior release and fusion is sometimes required in pediatric patients with thoracic scoliosis. Typically, a formal anterior approach is performed through open thoracotomy or video-assisted thoracoscopic surgery. The authors recently developed a technique for anterior release and fusion in thoracic scoliosis referred to as "posterior convex release and interbody fusion" (PCRIF). This technique is performed via the posterior-only approach typically used for posterior instrumentation and fusion and thus avoids a formal anterior approach. In this article the authors describe the technique and its use in 9 patients-to prevent a crankshaft phenomenon in 3 patients and to optimize the correction in 6 patients with a severe thoracic curve showing poor reducibility. After Ponte osteotomies at the levels requiring anterior release and fusion, intervertebral discs are approached from the convex side of the scoliosis. The annulus on the convex side of the scoliosis is incised from the lateral border of the pedicle to the lateral annulus while visualizing and protecting the pleura and spinal cord. The annulus in contact with the pleura and the anterior longitudinal ligament are removed before completing the discectomies and preparing the endplates. The PCRIF was performed at 3 levels in 4 patients and at 4 levels in 5 patients. Mean correction of the main thoracic curve, blood loss, and length of stay were 74.9%, 1290 ml, and 7.6 days, respectively. No neurological deficit, implant failure, or pseudarthrosis was observed at the last follow-up. Two patients had pleural effusion postoperatively, with 1 of them requiring placement of a chest tube. One patient had pulmonary edema secondary to fluid overload, while another patient underwent reoperation for a deep wound infection 3 weeks after the initial surgery. The technique is primarily indicated in skeletally immature patients with open triradiate cartilage and/or severe scoliosis. It can be particularly useful if there is significant vertebral rotation because access to the disc and anterior longitudinal ligament from the convex side will become safer. The PCRIF is an alternative to the formal anterior approach and does not require repositioning between the anterior and posterior stages, which prolongs the surgery and can be associated with an increased complication rate. The procedure can be done in the presence of preexisting pulmonary morbidity such as pleural adhesions and decreased pulmonary function because it does not require mobilization of the lung or single-lung ventilation. However, PCRIF can still be associated with pulmonary complications such as a pleural effusion, and care should be taken to avoid iatrogenic injury to the pleura. Placement of a deep wound drain at the level of the PCRIF is strongly recommended if postoperative bleeding is anticipated, to decrease the risk of pleural effusion.

TH-EF-BRB-05: 4pi Non-Coplanar IMRT Beam Angle Selection by Convex Optimization with Group Sparsity Penalty

DOE Office of Scientific and Technical Information (OSTI.GOV)

O’Connor, D; Nguyen, D; Voronenko, Y

Purpose: Integrated beam orientation and fluence map optimization is expected to be the foundation of robust automated planning but existing heuristic methods do not promise global optimality. We aim to develop a new method for beam angle selection in 4π non-coplanar IMRT systems based on solving (globally) a single convex optimization problem, and to demonstrate the effectiveness of the method by comparison with a state of the art column generation method for 4π beam angle selection. Methods: The beam angle selection problem is formulated as a large scale convex fluence map optimization problem with an additional group sparsity term thatmore » encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated first-order method, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The beam angle selection and fluence map optimization algorithm is used to create non-coplanar 4π treatment plans for several cases (including head and neck, lung, and prostate cases) and the resulting treatment plans are compared with 4π treatment plans created using the column generation algorithm. Results: In our experiments the treatment plans created using the group sparsity method meet or exceed the dosimetric quality of plans created using the column generation algorithm, which was shown superior to clinical plans. Moreover, the group sparsity approach converges in about 3 minutes in these cases, as compared with runtimes of a few hours for the column generation method. Conclusion: This work demonstrates the first non-greedy approach to non-coplanar beam angle selection, based on convex optimization, for 4π IMRT systems. The method given here improves both treatment plan quality and runtime as compared with a state of the art column generation algorithm. When the group sparsity term is set to zero, we obtain an excellent method for fluence map optimization, useful when beam angles have already been selected. NIH R43CA183390, NIH R01CA188300, Varian Medical Systems; Part of this research took place while D. O’Connor was a summer intern at RefleXion Medical.« less

Maximally dense packings of two-dimensional convex and concave noncircular particles.

PubMed

Atkinson, Steven; Jiao, Yang; Torquato, Salvatore

2012-09-01

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London) 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space R(d). While the original implementation was designed to study spheres and convex polyhedra in d≥3, our implementation focuses on d=2 and extends the algorithm to include both concave polygons and certain complex convex or concave nonpolygonal particle shapes. We verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons, then employ it to suggest dense packing arrangements of congruent copies of certain families of concave crosses, convex and concave curved triangles (incorporating shapes resembling the Mercedes-Benz logo), and "moonlike" shapes. Analytical constructions are determined subsequently to obtain the densest known packings of these particle shapes. For the examples considered, we find that the densest packings of both convex and concave particles with central symmetry are achieved by their corresponding optimal Bravais lattice packings; for particles lacking central symmetry, the densest packings obtained are nonlattice periodic packings, which are consistent with recently-proposed general organizing principles for hard particles. Moreover, we find that the densest known packings of certain curved triangles are periodic with a four-particle basis, and we find that the densest known periodic packings of certain moonlike shapes possess no inherent symmetries. Our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures.

Maximally dense packings of two-dimensional convex and concave noncircular particles

NASA Astrophysics Data System (ADS)

Atkinson, Steven; Jiao, Yang; Torquato, Salvatore

2012-09-01

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London)NATUAS0028-083610.1038/nature08239 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space Rd. While the original implementation was designed to study spheres and convex polyhedra in d≥3, our implementation focuses on d=2 and extends the algorithm to include both concave polygons and certain complex convex or concave nonpolygonal particle shapes. We verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons, then employ it to suggest dense packing arrangements of congruent copies of certain families of concave crosses, convex and concave curved triangles (incorporating shapes resembling the Mercedes-Benz logo), and “moonlike” shapes. Analytical constructions are determined subsequently to obtain the densest known packings of these particle shapes. For the examples considered, we find that the densest packings of both convex and concave particles with central symmetry are achieved by their corresponding optimal Bravais lattice packings; for particles lacking central symmetry, the densest packings obtained are nonlattice periodic packings, which are consistent with recently-proposed general organizing principles for hard particles. Moreover, we find that the densest known packings of certain curved triangles are periodic with a four-particle basis, and we find that the densest known periodic packings of certain moonlike shapes possess no inherent symmetries. Our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures.

Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation

DOE PAGES

Shen, Xinyue; Krim, Hamid; Gu, Yuantao

2016-03-01

Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. Here in this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints onmore » the Grassmann manifold, as well as the bilinearity in the penalty caused by the subspace bases and coefficients. Nevertheless, numerical experiments verify that the proposed algorithm, which provides elegant solutions to the sub-problems in each step, is able to de-couple the subspaces and pursue each of them under time-efficient parallel computation.« less

Energy optimization in mobile sensor networks

NASA Astrophysics Data System (ADS)

Yu, Shengwei

Mobile sensor networks are considered to consist of a network of mobile robots, each of which has computation, communication and sensing capabilities. Energy efficiency is a critical issue in mobile sensor networks, especially when mobility (i.e., locomotion control), routing (i.e., communications) and sensing are unique characteristics of mobile robots for energy optimization. This thesis focuses on the problem of energy optimization of mobile robotic sensor networks, and the research results can be extended to energy optimization of a network of mobile robots that monitors the environment, or a team of mobile robots that transports materials from stations to stations in a manufacturing environment. On the energy optimization of mobile robotic sensor networks, our research focuses on the investigation and development of distributed optimization algorithms to exploit the mobility of robotic sensor nodes for network lifetime maximization. In particular, the thesis studies these five problems: 1. Network-lifetime maximization by controlling positions of networked mobile sensor robots based on local information with distributed optimization algorithms; 2. Lifetime maximization of mobile sensor networks with energy harvesting modules; 3. Lifetime maximization using joint design of mobility and routing; 4. Optimal control for network energy minimization; 5. Network lifetime maximization in mobile visual sensor networks. In addressing the first problem, we consider only the mobility strategies of the robotic relay nodes in a mobile sensor network in order to maximize its network lifetime. By using variable substitutions, the original problem is converted into a convex problem, and a variant of the sub-gradient method for saddle-point computation is developed for solving this problem. An optimal solution is obtained by the method. Computer simulations show that mobility of robotic sensors can significantly prolong the lifetime of the whole robotic sensor network while consuming negligible amount of energy for mobility cost. For the second problem, the problem is extended to accommodate mobile robotic nodes with energy harvesting capability, which makes it a non-convex optimization problem. The non-convexity issue is tackled by using the existing sequential convex approximation method, based on which we propose a novel procedure of modified sequential convex approximation that has fast convergence speed. For the third problem, the proposed procedure is used to solve another challenging non-convex problem, which results in utilizing mobility and routing simultaneously in mobile robotic sensor networks to prolong the network lifetime. The results indicate that joint design of mobility and routing has an edge over other methods in prolonging network lifetime, which is also the justification for the use of mobility in mobile sensor networks for energy efficiency purpose. For the fourth problem, we include the dynamics of the robotic nodes in the problem by modeling the networked robotic system using hybrid systems theory. A novel distributed method for the networked hybrid system is used to solve the optimal moving trajectories for robotic nodes and optimal network links, which are not answered by previous approaches. Finally, the fact that mobility is more effective in prolonging network lifetime for a data-intensive network leads us to apply our methods to study mobile visual sensor networks, which are useful in many applications. We investigate the joint design of mobility, data routing, and encoding power to help improving the video quality while maximizing the network lifetime. This study leads to a better understanding of the role mobility can play in data-intensive surveillance sensor networks.

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants.

PubMed

Córcoles, Juan; Zastrow, Earl; Kuster, Niels

2015-09-21

Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient's anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant's RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B(1)(+) field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient's anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.

Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants

NASA Astrophysics Data System (ADS)

Córcoles, Juan; Zastrow, Earl; Kuster, Niels

2015-09-01

Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient’s anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant’s RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B1+ field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient’s anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.

Convex Regression with Interpretable Sharp Partitions

PubMed Central

Petersen, Ashley; Simon, Noah; Witten, Daniela

2016-01-01

We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set. PMID:27635120

A novel baseline correction method using convex optimization framework in laser-induced breakdown spectroscopy quantitative analysis

NASA Astrophysics Data System (ADS)

Yi, Cancan; Lv, Yong; Xiao, Han; Ke, Ke; Yu, Xun

2017-12-01

For laser-induced breakdown spectroscopy (LIBS) quantitative analysis technique, baseline correction is an essential part for the LIBS data preprocessing. As the widely existing cases, the phenomenon of baseline drift is generated by the fluctuation of laser energy, inhomogeneity of sample surfaces and the background noise, which has aroused the interest of many researchers. Most of the prevalent algorithms usually need to preset some key parameters, such as the suitable spline function and the fitting order, thus do not have adaptability. Based on the characteristics of LIBS, such as the sparsity of spectral peaks and the low-pass filtered feature of baseline, a novel baseline correction and spectral data denoising method is studied in this paper. The improved technology utilizes convex optimization scheme to form a non-parametric baseline correction model. Meanwhile, asymmetric punish function is conducted to enhance signal-noise ratio (SNR) of the LIBS signal and improve reconstruction precision. Furthermore, an efficient iterative algorithm is applied to the optimization process, so as to ensure the convergence of this algorithm. To validate the proposed method, the concentration analysis of Chromium (Cr),Manganese (Mn) and Nickel (Ni) contained in 23 certified high alloy steel samples is assessed by using quantitative models with Partial Least Squares (PLS) and Support Vector Machine (SVM). Because there is no prior knowledge of sample composition and mathematical hypothesis, compared with other methods, the method proposed in this paper has better accuracy in quantitative analysis, and fully reflects its adaptive ability.

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Parameterized LMI Based Diagonal Dominance Compensator Study for Polynomial Linear Parameter Varying System

NASA Astrophysics Data System (ADS)

Han, Xiaobao; Li, Huacong; Jia, Qiusheng

2017-12-01

For dynamic decoupling of polynomial linear parameter varying(PLPV) system, a robust dominance pre-compensator design method is given. The parameterized precompensator design problem is converted into an optimal problem constrained with parameterized linear matrix inequalities(PLMI) by using the conception of parameterized Lyapunov function(PLF). To solve the PLMI constrained optimal problem, the precompensator design problem is reduced into a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a new constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator is achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation on a turbofan engine PLPV model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr; Li, Juan, E-mail: juanli@sdu.edu.cn; Ma, Jin, E-mail: jinma@usc.edu

In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and wemore » extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.« less

Optimal Power Flow for Distribution Systems under Uncertain Forecasts: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

2016-12-01

The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhou, Xinyang; Liu, Zhiyuan

This paper considers distribution networks with distributed energy resources and discrete-rate loads, and designs an incentive-based algorithm that allows the network operator and the customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Four major challenges include: (1) the non-convexity from discrete decision variables, (2) the non-convexity due to a Stackelberg game structure, (3) unavailable private information from customers, and (4) different update frequency from two types of devices. In this paper, we first make convex relaxation for discrete variables, then reformulate the non-convex structure into a convex optimization problem together withmore » pricing/reward signal design, and propose a distributed stochastic dual algorithm for solving the reformulated problem while restoring feasible power rates for discrete devices. By doing so, we are able to statistically achieve the solution of the reformulated problem without exposure of any private information from customers. Stability of the proposed schemes is analytically established and numerically corroborated.« less

Fast alternating projection methods for constrained tomographic reconstruction

PubMed Central

Liu, Li; Han, Yongxin

2017-01-01

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification. PMID:28253298

Cryogenic Tank Structure Sizing With Structural Optimization Method

NASA Technical Reports Server (NTRS)

Wang, J. T.; Johnson, T. F.; Sleight, D. W.; Saether, E.

2001-01-01

Structural optimization methods in MSC /NASTRAN are used to size substructures and to reduce the weight of a composite sandwich cryogenic tank for future launch vehicles. Because the feasible design space of this problem is non-convex, many local minima are found. This non-convex problem is investigated in detail by conducting a series of analyses along a design line connecting two feasible designs. Strain constraint violations occur for some design points along the design line. Since MSC/NASTRAN uses gradient-based optimization procedures. it does not guarantee that the lowest weight design can be found. In this study, a simple procedure is introduced to create a new starting point based on design variable values from previous optimization analyses. Optimization analysis using this new starting point can produce a lower weight design. Detailed inputs for setting up the MSC/NASTRAN optimization analysis and final tank design results are presented in this paper. Approaches for obtaining further weight reductions are also discussed.

Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

PubMed

Bian, Wei; Ma, Litao; Qin, Sitian; Xue, Xiaoping

2018-05-01

In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included. Copyright © 2018 Elsevier Ltd. All rights reserved.

GASPACHO: a generic automatic solver using proximal algorithms for convex huge optimization problems

NASA Astrophysics Data System (ADS)

Goossens, Bart; Luong, Hiêp; Philips, Wilfried

2017-08-01

Many inverse problems (e.g., demosaicking, deblurring, denoising, image fusion, HDR synthesis) share various similarities: degradation operators are often modeled by a specific data fitting function while image prior knowledge (e.g., sparsity) is incorporated by additional regularization terms. In this paper, we investigate automatic algorithmic techniques for evaluating proximal operators. These algorithmic techniques also enable efficient calculation of adjoints from linear operators in a general matrix-free setting. In particular, we study the simultaneous-direction method of multipliers (SDMM) and the parallel proximal algorithm (PPXA) solvers and show that the automatically derived implementations are well suited for both single-GPU and multi-GPU processing. We demonstrate this approach for an Electron Microscopy (EM) deconvolution problem.

Density of convex intersections and applications

PubMed Central

Rautenberg, C. N.; Rösel, S.

2017-01-01

In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems. PMID:28989301

Towards optimal experimental tests on the reality of the quantum state

NASA Astrophysics Data System (ADS)

Knee, George C.

2017-02-01

The Barrett-Cavalcanti-Lal-Maroney (BCLM) argument stands as the most effective means of demonstrating the reality of the quantum state. Its advantages include being derived from very few assumptions, and a robustness to experimental error. Finding the best way to implement the argument experimentally is an open problem, however, and involves cleverly choosing sets of states and measurements. I show that techniques from convex optimisation theory can be leveraged to numerically search for these sets, which then form a recipe for experiments that allow for the strongest statements about the ontology of the wavefunction to be made. The optimisation approach presented is versatile, efficient and can take account of the finite errors present in any real experiment. I find significantly improved low-cardinality sets which are guaranteed partially optimal for a BCLM test in low Hilbert space dimension. I further show that mixed states can be more optimal than pure states.

Device-Independent Tests of Entropy

NASA Astrophysics Data System (ADS)

Chaves, Rafael; Brask, Jonatan Bohr; Brunner, Nicolas

2015-09-01

We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical communication, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, J.V.

The published work on exact penalization is indeed vast. Recently this work has indicated an intimate relationship between exact penalization, Lagrange multipliers, and problem stability or calmness. In the present work we chronicle this development within a simple idealized problem framework, wherein we unify, extend, and refine much of the known theory. In particular, most of the foundations for constrained optimization are developed with the aid of exact penalization techniques. Our approach is highly geometric and is based upon the elementary subdifferential theory for distance functions. It is assumed that the reader is familiar with the theory of convex setsmore » and functions. 54 refs.« less

Shape complexes: the intersection of label orderings and star convexity constraints in continuous max-flow medical image segmentation

PubMed Central

Baxter, John S. H.; Inoue, Jiro; Drangova, Maria; Peters, Terry M.

2016-01-01

Abstract. Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. The concept of “shape complexes,” which combine geodesic star convexity with extendable continuous max-flow solvers, is presented. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous approaches required computationally expensive coordinate system warping, which are ill-defined and ambiguous in the general case. These shape complexes are demonstrated in a set of synthetic images as well as vessel segmentation in ultrasound, valve segmentation in ultrasound, and atrial wall segmentation from contrast-enhanced CT. Shape complexes represent an extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems. PMID:28018937

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods

PubMed Central

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-01-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.

PubMed

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-05-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L 2 -norm regularization. However, sparse representation methods via L 1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L 1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.

On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov's fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization.

On the Convergence Analysis of the Optimized Gradient Method

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2016-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov’s fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization. PMID:28461707

Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

2016-09-01

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

DOE Office of Scientific and Technical Information (OSTI.GOV)

DallAnese, Emiliano; Baker, Kyri; Summers, Tyler

This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrarymore » distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.« less

Regularized Embedded Multiple Kernel Dimensionality Reduction for Mine Signal Processing.

PubMed

Li, Shuang; Liu, Bing; Zhang, Chen

2016-01-01

Traditional multiple kernel dimensionality reduction models are generally based on graph embedding and manifold assumption. But such assumption might be invalid for some high-dimensional or sparse data due to the curse of dimensionality, which has a negative influence on the performance of multiple kernel learning. In addition, some models might be ill-posed if the rank of matrices in their objective functions was not high enough. To address these issues, we extend the traditional graph embedding framework and propose a novel regularized embedded multiple kernel dimensionality reduction method. Different from the conventional convex relaxation technique, the proposed algorithm directly takes advantage of a binary search and an alternative optimization scheme to obtain optimal solutions efficiently. The experimental results demonstrate the effectiveness of the proposed method for supervised, unsupervised, and semisupervised scenarios.

Photon-efficient super-resolution laser radar

NASA Astrophysics Data System (ADS)

Shin, Dongeek; Shapiro, Jeffrey H.; Goyal, Vivek K.

2017-08-01

The resolution achieved in photon-efficient active optical range imaging systems can be low due to non-idealities such as propagation through a diffuse scattering medium. We propose a constrained optimization-based frame- work to address extremes in scarcity of photons and blurring by a forward imaging kernel. We provide two algorithms for the resulting inverse problem: a greedy algorithm, inspired by sparse pursuit algorithms; and a convex optimization heuristic that incorporates image total variation regularization. We demonstrate that our framework outperforms existing deconvolution imaging techniques in terms of peak signal-to-noise ratio. Since our proposed method is able to super-resolve depth features using small numbers of photon counts, it can be useful for observing fine-scale phenomena in remote sensing through a scattering medium and through-the-skin biomedical imaging applications.

A Polyhedral Outer-approximation, Dynamic-discretization optimization solver, 1.x

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, Rusell; Nagarajan, Harsha; Sundar, Kaarthik

2017-09-25

In this software, we implement an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) to global optimality. The algorithm combines ideas that exploit the structure of convex relaxations to MINLPs and bound tightening procedures

Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms With Directed Gossip Communication

NASA Astrophysics Data System (ADS)

Jakovetic, Dusan; Xavier, João; Moura, José M. F.

2011-08-01

We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms. PMID:24077658

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks.

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.

2014-01-01

This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.

Resource allocation in shared spectrum access communications for operators with diverse service requirements

NASA Astrophysics Data System (ADS)

Kibria, Mirza Golam; Villardi, Gabriel Porto; Ishizu, Kentaro; Kojima, Fumihide; Yano, Hiroyuki

2016-12-01

In this paper, we study inter-operator spectrum sharing and intra-operator resource allocation in shared spectrum access communication systems and propose efficient dynamic solutions to address both inter-operator and intra-operator resource allocation optimization problems. For inter-operator spectrum sharing, we present two competent approaches, namely the subcarrier gain-based sharing and fragmentation-based sharing, which carry out fair and flexible allocation of the available shareable spectrum among the operators subject to certain well-defined sharing rules, traffic demands, and channel propagation characteristics. The subcarrier gain-based spectrum sharing scheme has been found to be more efficient in terms of achieved throughput. However, the fragmentation-based sharing is more attractive in terms of computational complexity. For intra-operator resource allocation, we consider resource allocation problem with users' dissimilar service requirements, where the operator supports users with delay constraint and non-delay constraint service requirements, simultaneously. This optimization problem is a mixed-integer non-linear programming problem and non-convex, which is computationally very expensive, and the complexity grows exponentially with the number of integer variables. We propose less-complex and efficient suboptimal solution based on formulating exact linearization, linear approximation, and convexification techniques for the non-linear and/or non-convex objective functions and constraints. Extensive simulation performance analysis has been carried out that validates the efficiency of the proposed solution.

The Role of Hellinger Processes in Mathematical Finance

NASA Astrophysics Data System (ADS)

Choulli, T.; Hurd, T. R.

2001-09-01

This paper illustrates the natural role that Hellinger processes can play in solving problems from ¯nance. We propose an extension of the concept of Hellinger process applicable to entropy distance and f-divergence distances, where f is a convex logarithmic function or a convex power function with general order q, 0 6= q < 1. These concepts lead to a new approach to Merton's optimal portfolio problem and its dual in general L¶evy markets.

Optimal GENCO bidding strategy

NASA Astrophysics Data System (ADS)

Gao, Feng

Electricity industries worldwide are undergoing a period of profound upheaval. The conventional vertically integrated mechanism is being replaced by a competitive market environment. Generation companies have incentives to apply novel technologies to lower production costs, for example: Combined Cycle units. Economic dispatch with Combined Cycle units becomes a non-convex optimization problem, which is difficult if not impossible to solve by conventional methods. Several techniques are proposed here: Mixed Integer Linear Programming, a hybrid method, as well as Evolutionary Algorithms. Evolutionary Algorithms share a common mechanism, stochastic searching per generation. The stochastic property makes evolutionary algorithms robust and adaptive enough to solve a non-convex optimization problem. This research implements GA, EP, and PS algorithms for economic dispatch with Combined Cycle units, and makes a comparison with classical Mixed Integer Linear Programming. The electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models. This research identifies a proper SFE model, which can be applied to a multiple period situation. The equilibrium condition using discrete time optimal control is then developed for fuel resource constraints. Finally, the research discusses the issues of multiple equilibria and mixed strategies, which are caused by the transmission network. Additionally, an advantage of the proposed model for merchant transmission planning is discussed. A market simulator is a valuable training and evaluation tool to assist sellers, buyers, and regulators to understand market performance and make better decisions. A traditional optimization model may not be enough to consider the distributed, large-scale, and complex energy market. This research compares the performance and searching paths of different artificial life techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm (PS), and look for a proper method to emulate Generation Companies' (GENCOs) bidding strategies. After deregulation, GENCOs face risk and uncertainty associated with the fast-changing market environment. A profit-based bidding decision support system is critical for GENCOs to keep a competitive position in the new environment. Most past research do not pay special attention to the piecewise staircase characteristic of generator offer curves. This research proposes an optimal bidding strategy based on Parametric Linear Programming. The proposed algorithm is able to handle actual piecewise staircase energy offer curves. The proposed method is then extended to incorporate incomplete information based on Decision Analysis. Finally, the author develops an optimal bidding tool (GenBidding) and applies it to the RTS96 test system.

Scaling of Convex Hull Volume to Body Mass in Modern Primates, Non-Primate Mammals and Birds

PubMed Central

Brassey, Charlotte A.; Sellers, William I.

2014-01-01

The volumetric method of ‘convex hulling’ has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol CH) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (M b) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol CH has remained unclear. Specifically, when vol CH scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of M b to vol CH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r 2 = 0.97–0.99) and low mean percentage prediction error (11–20%). Results suggest non-primate mammals scale body mass to vol CH isometrically (b = 0.92, 95%CI = 0.85–1.00, p = 0.08). Birds scale body mass to vol CH with negative allometry (b = 0.81, 95%CI = 0.70–0.91, p = 0.011) and apparent density (vol CH/M b) therefore decreases with mass (r 2 = 0.36, p<0.05). In contrast, primates scale body mass to vol CH with positive allometry (b = 1.07, 95%CI = 1.01–1.12, p = 0.05) and apparent density therefore increases with size (r 2 = 0.46, p = 0.025). We interpret such departures from isometry in the context of the ‘missing mass’ of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat. PMID:24618736

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

Convex Optimization over Classes of Multiparticle Entanglement

NASA Astrophysics Data System (ADS)

Shang, Jiangwei; Gühne, Otfried

2018-02-01

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010), 10.1103/PhysRevLett.105.130501].

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamzam, Ahmed, S.; Zhaoy, Changhong; Dall'Anesey, Emiliano

This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated usingmore » two unbalanced multiphase distribution feeders with both wye and delta connections.« less

Interactive Reference Point Procedure Based on the Conic Scalarizing Function

PubMed Central

2014-01-01

In multiobjective optimization methods, multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions. The conic scalarizing function is a general characterization of Benson proper efficient solutions of non-convex multiobjective problems in terms of saddle points of scalar Lagrangian functions. This approach preserves convexity. The conic scalarizing function, as a part of a posteriori or a priori methods, has successfully been applied to several real-life problems. In this paper, we propose a conic scalarizing function based interactive reference point procedure where the decision maker actively takes part in the solution process and directs the search according to her or his preferences. An algorithmic framework for the interactive solution of multiple objective optimization problems is presented and is utilized for solving some illustrative examples. PMID:24723795

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao Yunbin, E-mail: zhaoyy@maths.bham.ac.u

2010-12-15

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the conditionmore » number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.« less

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

NASA Astrophysics Data System (ADS)

Hernandez, Monica

2017-12-01

This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

Weighted mining of massive collections of [Formula: see text]-values by convex optimization.

PubMed

Dobriban, Edgar

2018-06-01

Researchers in data-rich disciplines-think of computational genomics and observational cosmology-often wish to mine large bodies of [Formula: see text]-values looking for significant effects, while controlling the false discovery rate or family-wise error rate. Increasingly, researchers also wish to prioritize certain hypotheses, for example, those thought to have larger effect sizes, by upweighting, and to impose constraints on the underlying mining, such as monotonicity along a certain sequence. We introduce Princessp , a principled method for performing weighted multiple testing by constrained convex optimization. Our method elegantly allows one to prioritize certain hypotheses through upweighting and to discount others through downweighting, while constraining the underlying weights involved in the mining process. When the [Formula: see text]-values derive from monotone likelihood ratio families such as the Gaussian means model, the new method allows exact solution of an important optimal weighting problem previously thought to be non-convex and computationally infeasible. Our method scales to massive data set sizes. We illustrate the applications of Princessp on a series of standard genomics data sets and offer comparisons with several previous 'standard' methods. Princessp offers both ease of operation and the ability to scale to extremely large problem sizes. The method is available as open-source software from github.com/dobriban/pvalue_weighting_matlab (accessed 11 October 2017).

Maximum Margin Clustering of Hyperspectral Data

NASA Astrophysics Data System (ADS)

Niazmardi, S.; Safari, A.; Homayouni, S.

2013-09-01

In recent decades, large margin methods such as Support Vector Machines (SVMs) are supposed to be the state-of-the-art of supervised learning methods for classification of hyperspectral data. However, the results of these algorithms mainly depend on the quality and quantity of available training data. To tackle down the problems associated with the training data, the researcher put effort into extending the capability of large margin algorithms for unsupervised learning. One of the recent proposed algorithms is Maximum Margin Clustering (MMC). The MMC is an unsupervised SVMs algorithm that simultaneously estimates both the labels and the hyperplane parameters. Nevertheless, the optimization of the MMC algorithm is a non-convex problem. Most of the existing MMC methods rely on the reformulating and the relaxing of the non-convex optimization problem as semi-definite programs (SDP), which are computationally very expensive and only can handle small data sets. Moreover, most of these algorithms are two-class classification, which cannot be used for classification of remotely sensed data. In this paper, a new MMC algorithm is used that solve the original non-convex problem using Alternative Optimization method. This algorithm is also extended for multi-class classification and its performance is evaluated. The results of the proposed algorithm show that the algorithm has acceptable results for hyperspectral data clustering.

Joint pricing and production management: a geometric programming approach with consideration of cubic production cost function

NASA Astrophysics Data System (ADS)

Sadjadi, Seyed Jafar; Hamidi Hesarsorkh, Aghil; Mohammadi, Mehdi; Bonyadi Naeini, Ali

2015-06-01

Coordination and harmony between different departments of a company can be an important factor in achieving competitive advantage if the company corrects alignment between strategies of different departments. This paper presents an integrated decision model based on recent advances of geometric programming technique. The demand of a product considers as a power function of factors such as product's price, marketing expenditures, and consumer service expenditures. Furthermore, production cost considers as a cubic power function of outputs. The model will be solved by recent advances in convex optimization tools. Finally, the solution procedure is illustrated by numerical example.

[Design method of convex master gratings for replicating flat-field concave gratings].

PubMed

Zhou, Qian; Li, Li-Feng

2009-08-01

Flat-field concave diffraction grating is the key device of a portable grating spectrometer with the advantage of integrating dispersion, focusing and flat-field in a single device. It directly determines the quality of a spectrometer. The most important two performances determining the quality of the spectrometer are spectral image quality and diffraction efficiency. The diffraction efficiency of a grating depends mainly on its groove shape. But it has long been a problem to get a uniform predetermined groove shape across the whole concave grating area, because the incident angle of the ion beam is restricted by the curvature of the concave substrate, and this severely limits the diffraction efficiency and restricts the application of concave gratings. The authors present a two-step method for designing convex gratings, which are made holographically with two exposure point sources placed behind a plano-convex transparent glass substrate, to solve this problem. The convex gratings are intended to be used as the master gratings for making aberration-corrected flat-field concave gratings. To achieve high spectral image quality for the replicated concave gratings, the refraction effect at the planar back surface and the extra optical path lengths through the substrate thickness experienced by the two divergent recording beams are considered during optimization. This two-step method combines the optical-path-length function method and the ZEMAX software to complete the optimization with a high success rate and high efficiency. In the first step, the optical-path-length function method is used without considering the refraction effect to get an approximate optimization result. In the second step, the approximate result of the first step is used as the initial value for ZEMAX to complete the optimization including the refraction effect. An example of design problem was considered. The simulation results of ZEMAX proved that the spectral image quality of a replicated concave grating is comparable with that of a directly recorded concave grating.

Efficient Convex Optimization for Energy-Based Acoustic Sensor Self-Localization and Source Localization in Sensor Networks.

PubMed

Yan, Yongsheng; Wang, Haiyan; Shen, Xiaohong; Leng, Bing; Li, Shuangquan

2018-05-21

The energy reading has been an efficient and attractive measure for collaborative acoustic source localization in practical application due to its cost saving in both energy and computation capability. The maximum likelihood problems by fusing received acoustic energy readings transmitted from local sensors are derived. Aiming to efficiently solve the nonconvex objective of the optimization problem, we present an approximate estimator of the original problem. Then, a direct norm relaxation and semidefinite relaxation, respectively, are utilized to derive the second-order cone programming, semidefinite programming or mixture of them for both cases of sensor self-location and source localization. Furthermore, by taking the colored energy reading noise into account, several minimax optimization problems are formulated, which are also relaxed via the direct norm relaxation and semidefinite relaxation respectively into convex optimization problems. Performance comparison with the existing acoustic energy-based source localization methods is given, where the results show the validity of our proposed methods.

Efficient Convex Optimization for Energy-Based Acoustic Sensor Self-Localization and Source Localization in Sensor Networks

PubMed Central

Yan, Yongsheng; Wang, Haiyan; Shen, Xiaohong; Leng, Bing; Li, Shuangquan

2018-01-01

The energy reading has been an efficient and attractive measure for collaborative acoustic source localization in practical application due to its cost saving in both energy and computation capability. The maximum likelihood problems by fusing received acoustic energy readings transmitted from local sensors are derived. Aiming to efficiently solve the nonconvex objective of the optimization problem, we present an approximate estimator of the original problem. Then, a direct norm relaxation and semidefinite relaxation, respectively, are utilized to derive the second-order cone programming, semidefinite programming or mixture of them for both cases of sensor self-location and source localization. Furthermore, by taking the colored energy reading noise into account, several minimax optimization problems are formulated, which are also relaxed via the direct norm relaxation and semidefinite relaxation respectively into convex optimization problems. Performance comparison with the existing acoustic energy-based source localization methods is given, where the results show the validity of our proposed methods. PMID:29883410

Image reconstruction and scan configurations enabled by optimization-based algorithms in multispectral CT

NASA Astrophysics Data System (ADS)

Chen, Buxin; Zhang, Zheng; Sidky, Emil Y.; Xia, Dan; Pan, Xiaochuan

2017-11-01

Optimization-based algorithms for image reconstruction in multispectral (or photon-counting) computed tomography (MCT) remains a topic of active research. The challenge of optimization-based image reconstruction in MCT stems from the inherently non-linear data model that can lead to a non-convex optimization program for which no mathematically exact solver seems to exist for achieving globally optimal solutions. In this work, based upon a non-linear data model, we design a non-convex optimization program, derive its first-order-optimality conditions, and propose an algorithm to solve the program for image reconstruction in MCT. In addition to consideration of image reconstruction for the standard scan configuration, the emphasis is on investigating the algorithm’s potential for enabling non-standard scan configurations with no or minimum hardware modification to existing CT systems, which has potential practical implications for lowered hardware cost, enhanced scanning flexibility, and reduced imaging dose/time in MCT. Numerical studies are carried out for verification of the algorithm and its implementation, and for a preliminary demonstration and characterization of the algorithm in reconstructing images and in enabling non-standard configurations with varying scanning angular range and/or x-ray illumination coverage in MCT.

Chance-Constrained Guidance With Non-Convex Constraints

NASA Technical Reports Server (NTRS)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.

PubMed

Ding, Shuguang; Nie, Xiangli; Qiao, Hong; Zhang, Bo

2018-04-01

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.

Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities

DOE PAGES

Coffrin, Carleton James; Hijazi, Hassan L; Van Hentenryck, Pascal R

2016-12-01

Here this work revisits the Semidefine Programming (SDP) relaxation of the AC power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the Convex Quadratic (QC) relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% ofmore » the open cases considered, leaving only 8 for future investigation.« less

Liquid phase heteroepitaxial growth on convex substrate using binary phase field crystal model

NASA Astrophysics Data System (ADS)

Lu, Yanli; Zhang, Tinghui; Chen, Zheng

2018-06-01

The liquid phase heteroepitaxial growth on convex substrate is investigated with the binary phase field crystal (PFC) model. The paper aims to focus on the transformation of the morphology of epitaxial films on convex substrate with two different radiuses of curvature (Ω) as well as influences of substrate vicinal angles on films growth. It is found that films growth experience different stages on convex substrate with different radiuses of curvature (Ω). For Ω = 512 Δx , the process of epitaxial film growth includes four stages: island coupled with layer-by-layer growth, layer-by-layer growth, island coupled with layer-by-layer growth, layer-by-layer growth. For Ω = 1024 Δx , film growth only experience islands growth and layer-by-layer growth. Also, substrate vicinal angle (π) is an important parameter for epitaxial film growth. We find the film can grow well when π = 2° for Ω = 512 Δx , while the optimized film can be obtained when π = 4° for Ω = 512 Δx .

Semilinear (topological) spaces and applications

NASA Technical Reports Server (NTRS)

Prakash, P.; Sertel, M. R.

1971-01-01

Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.

Lanczos eigensolution method for high-performance computers

NASA Technical Reports Server (NTRS)

Bostic, Susan W.

1991-01-01

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

A Novel Method Using Abstract Convex Underestimation in Ab-Initio Protein Structure Prediction for Guiding Search in Conformational Feature Space.

PubMed

Hao, Xiao-Hu; Zhang, Gui-Jun; Zhou, Xiao-Gen; Yu, Xu-Feng

2016-01-01

To address the searching problem of protein conformational space in ab-initio protein structure prediction, a novel method using abstract convex underestimation (ACUE) based on the framework of evolutionary algorithm was proposed. Computing such conformations, essential to associate structural and functional information with gene sequences, is challenging due to the high-dimensionality and rugged energy surface of the protein conformational space. As a consequence, the dimension of protein conformational space should be reduced to a proper level. In this paper, the high-dimensionality original conformational space was converted into feature space whose dimension is considerably reduced by feature extraction technique. And, the underestimate space could be constructed according to abstract convex theory. Thus, the entropy effect caused by searching in the high-dimensionality conformational space could be avoided through such conversion. The tight lower bound estimate information was obtained to guide the searching direction, and the invalid searching area in which the global optimal solution is not located could be eliminated in advance. Moreover, instead of expensively calculating the energy of conformations in the original conformational space, the estimate value is employed to judge if the conformation is worth exploring to reduce the evaluation time, thereby making computational cost lower and the searching process more efficient. Additionally, fragment assembly and the Monte Carlo method are combined to generate a series of metastable conformations by sampling in the conformational space. The proposed method provides a novel technique to solve the searching problem of protein conformational space. Twenty small-to-medium structurally diverse proteins were tested, and the proposed ACUE method was compared with It Fix, HEA, Rosetta and the developed method LEDE without underestimate information. Test results show that the ACUE method can more rapidly and more efficiently obtain the near-native protein structure.

Optimal Path Determination for Flying Vehicle to Search an Object

NASA Astrophysics Data System (ADS)

Heru Tjahjana, R.; Heri Soelistyo U, R.; Ratnasari, L.; Irawanto, B.

2018-01-01

In this paper, a method to determine optimal path for flying vehicle to search an object is proposed. Background of the paper is controlling air vehicle to search an object. Optimal path determination is one of the most popular problem in optimization. This paper describe model of control design for a flying vehicle to search an object, and focus on the optimal path that used to search an object. In this paper, optimal control model is used to control flying vehicle to make the vehicle move in optimal path. If the vehicle move in optimal path, then the path to reach the searched object also optimal. The cost Functional is one of the most important things in optimal control design, in this paper the cost functional make the air vehicle can move as soon as possible to reach the object. The axis reference of flying vehicle uses N-E-D (North-East-Down) coordinate system. The result of this paper are the theorems which say that the cost functional make the control optimal and make the vehicle move in optimal path are proved analytically. The other result of this paper also shows the cost functional which used is convex. The convexity of the cost functional is use for guarantee the existence of optimal control. This paper also expose some simulations to show an optimal path for flying vehicle to search an object. The optimization method which used to find the optimal control and optimal path vehicle in this paper is Pontryagin Minimum Principle.

Ultrasound-guided Subclavian Vein Cannulation Using a Micro-Convex Ultrasound Probe

PubMed Central

Fair, James; Hirshberg, Eliotte L.; Grissom, Colin K.; Brown, Samuel M.

2014-01-01

Background: The subclavian vein is the preferred site for central venous catheter placement due to infection risk and patient comfort. Ultrasound guidance is useful in cannulation of other veins, but for the subclavian vein, current ultrasound-guided techniques using high-frequency linear array probes are generally limited to axillary vein cannulation. Methods: We report a series of patients who underwent clinically indicated subclavian venous catheter placement using a micro-convex pediatric probe for real-time guidance in the vein’s longitudinal axis. We identified rates of successful placement and complications by chart review. Results: Twenty-four catheters were placed using the micro-convex pediatric probe with confirmation of placement of the needle medial to the lateral border of the first rib. Sixteen of the catheters were placed by trainee physicians. In 23 patients, the catheter was placed without complication (hematoma, pneumothorax, infection). In one patient, the vein could not be safely cannulated without risk of arterial puncture, so an alternative site was selected. Conclusions: Infraclavicular subclavian vein cannulation using real-time ultrasound with a micro-convex pediatric probe appears to be a safe and effective method of placing subclavian vascular catheters. This technique merits further study to confirm safety and efficacy. PMID:24611628

Fluence map optimization (FMO) with dose-volume constraints in IMRT using the geometric distance sorting method.

PubMed

Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang

2012-10-21

A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose sorting method. By integrating a smart constraint adding/deleting scheme within the iteration framework, the new technique builds up an improved algorithm for solving the fluence map optimization with dose-volume constraints.

Method of constructing dished ion thruster grids to provide hole array spacing compensation

NASA Technical Reports Server (NTRS)

Banks, B. A. (Inventor)

1976-01-01

The center-to-center spacings of a photoresist pattern for an array of holes applied to a thin metal sheet are increased by uniformly stretching the thin metal sheet in all directions along the plane of the sheet. The uniform stretching is provided by securely clamping the periphery of the sheet and applying an annular force against the face of the sheet, within the periphery of the sheet and around the photoresist pattern. The technique is used in the construction of ion thruster grid units where the outer or downstream grid is subjected to uniform stretching prior to convex molding. The technique provides alignment of the holes of grid pairs so as to direct the ion beamlets in a direction parallel to the axis of the grid unit and thereby provide optimization of the available thrust.

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

NASA Technical Reports Server (NTRS)

Ortiz, Francisco

2004-01-01

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

A Framework for Multifaceted Evaluation of Student Models

ERIC Educational Resources Information Center

Huang, Yun; González-Brenes, José P.; Kumar, Rohit; Brusilovsky, Peter

2015-01-01

Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained…

Fabrication of ф 160 mm convex hyperbolic mirror for remote sensing instrument

NASA Astrophysics Data System (ADS)

Kuo, Ching-Hsiang; Yu, Zong-Ru; Ho, Cheng-Fang; Hsu, Wei-Yao; Chen, Fong-Zhi

2012-10-01

In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the Fabrication of ф160 mm Convex Hyperbolic Mirror for Remote Sensing Instrument160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.

A new corrective technique for adolescent idiopathic scoliosis: convex manipulation using 6.35 mm diameter pure titanium rod followed by concave fixation using 6.35 mm diameter titanium alloy

PubMed Central

2015-01-01

Background It has been thought that corrective posterior surgery for adolescent idiopathic scoliosis (AIS) should be started on the concave side because initial convex manipulation would increase the risk of vertebral malrotation, worsening the rib hump. With the many new materials, implants, and manipulation techniques (e.g., direct vertebral rotation) now available, we hypothesized that manipulating the convex side first is no longer taboo. Methods Our technique has two major facets. (1) Curve correction is started from the convex side with a derotation maneuver and in situ bending followed by concave rod application. (2) A 6.35 mm diameter pure titanium rod is used on the convex side and a 6.35 mm diameter titanium alloy rod on the concave side. Altogether, 52 patients were divided into two groups. Group N included 40 patients (3 male, 37 female; average age 15.9 years) of Lenke type 1 (23 patients), type 2 (2), type 3 (3), type 5 (10), type 6 (2). They were treated with a new technique using 6.35 mm diameter different-stiffness titanium rods. Group C included 12 patients (all female, average age 18.8 years) of Lenke type 1 (6 patients), type 2 (3), type 3 (1), type 5 (1), type 6 (1). They were treated with conventional methods using 5.5 mm diameter titanium alloy rods. Radiographic parameters (Cobb angle/thoracic kyphosis/correction rates) and perioperative data were retrospectively collected and analyzed. Results Preoperative main Cobb angles (groups N/C) were 56.8°/60.0°, which had improved to 15.2°/17.1° at the latest follow-up. Thoracic kyphosis increased from 16.8° to 21.3° in group N and from 16.0° to 23.4° in group C. Correction rates were 73.2% in group N and 71.7% in group C. There were no significant differences for either parameter. Mean operating time, however, was significantly shorter in group N (364 min) than in group C (456 min). Conclusion We developed a new corrective surgical technique for AIS using a 6.35 mm diameter pure titanium rod initially on the convex side. Correction rates in the coronal, sagittal, and axial planes were the same as those achieved with conventional methods, but the operation time was significantly shorter. PMID:25815053

The Iterative Reweighted Mixed-Norm Estimate for Spatio-Temporal MEG/EEG Source Reconstruction.

PubMed

Strohmeier, Daniel; Bekhti, Yousra; Haueisen, Jens; Gramfort, Alexandre

2016-10-01

Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, constraints are required. For the analysis of evoked brain activity, spatial sparsity of the neuronal activation is a common assumption. It is often taken into account using convex constraints based on the l 1 -norm. The resulting source estimates are however biased in amplitude and often suboptimal in terms of source selection due to high correlations in the forward model. In this work, we demonstrate that an inverse solver based on a block-separable penalty with a Frobenius norm per block and a l 0.5 -quasinorm over blocks addresses both of these issues. For solving the resulting non-convex optimization problem, we propose the iterative reweighted Mixed Norm Estimate (irMxNE), an optimization scheme based on iterative reweighted convex surrogate optimization problems, which are solved efficiently using a block coordinate descent scheme and an active set strategy. We compare the proposed sparse imaging method to the dSPM and the RAP-MUSIC approach based on two MEG data sets. We provide empirical evidence based on simulations and analysis of MEG data that the proposed method improves on the standard Mixed Norm Estimate (MxNE) in terms of amplitude bias, support recovery, and stability.

Constrained spacecraft reorientation using mixed integer convex programming

NASA Astrophysics Data System (ADS)

Tam, Margaret; Glenn Lightsey, E.

2016-10-01

A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.

JPEG2000-coded image error concealment exploiting convex sets projections.

PubMed

Atzori, Luigi; Ginesu, Giaime; Raccis, Alessio

2005-04-01

Transmission errors in JPEG2000 can be grouped into three main classes, depending on the affected area: LL, high frequencies at the lower decomposition levels, and high frequencies at the higher decomposition levels. The first type of errors are the most annoying but can be concealed exploiting the signal spatial correlation like in a number of techniques proposed in the past; the second are less annoying but more difficult to address; the latter are often imperceptible. In this paper, we address the problem of concealing the second class or errors when high bit-planes are damaged by proposing a new approach based on the theory of projections onto convex sets. Accordingly, the error effects are masked by iteratively applying two procedures: low-pass (LP) filtering in the spatial domain and restoration of the uncorrupted wavelet coefficients in the transform domain. It has been observed that a uniform LP filtering brought to some undesired side effects that negatively compensated the advantages. This problem has been overcome by applying an adaptive solution, which exploits an edge map to choose the optimal filter mask size. Simulation results demonstrated the efficiency of the proposed approach.

Computing the Feasible Spaces of Optimal Power Flow Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Molzahn, Daniel K.

The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem’s feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem’s inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC)more » algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. Here, the proposed algorithm is used to generate the feasible spaces of two small test cases.« less

Computing the Feasible Spaces of Optimal Power Flow Problems

DOE PAGES

Molzahn, Daniel K.

2017-03-15

The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem’s feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem’s inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC)more » algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. Here, the proposed algorithm is used to generate the feasible spaces of two small test cases.« less

A Convex Approach to Fault Tolerant Control

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Cox, David E.; Bauer, Frank (Technical Monitor)

2002-01-01

The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.

Distributed Optimization Design of Continuous-Time Multiagent Systems With Unknown-Frequency Disturbances.

PubMed

Wang, Xinghu; Hong, Yiguang; Yi, Peng; Ji, Haibo; Kang, Yu

2017-05-24

In this paper, a distributed optimization problem is studied for continuous-time multiagent systems with unknown-frequency disturbances. A distributed gradient-based control is proposed for the agents to achieve the optimal consensus with estimating unknown frequencies and rejecting the bounded disturbance in the semi-global sense. Based on convex optimization analysis and adaptive internal model approach, the exact optimization solution can be obtained for the multiagent system disturbed by exogenous disturbances with uncertain parameters.

A Subspace Semi-Definite programming-based Underestimation (SSDU) method for stochastic global optimization in protein docking*

PubMed Central

Nan, Feng; Moghadasi, Mohammad; Vakili, Pirooz; Vajda, Sandor; Kozakov, Dima; Ch. Paschalidis, Ioannis

2015-01-01

We propose a new stochastic global optimization method targeting protein docking problems. The method is based on finding a general convex polynomial underestimator to the binding energy function in a permissive subspace that possesses a funnel-like structure. We use Principal Component Analysis (PCA) to determine such permissive subspaces. The problem of finding the general convex polynomial underestimator is reduced into the problem of ensuring that a certain polynomial is a Sum-of-Squares (SOS), which can be done via semi-definite programming. The underestimator is then used to bias sampling of the energy function in order to recover a deep minimum. We show that the proposed method significantly improves the quality of docked conformations compared to existing methods. PMID:25914440

A vectorized Lanczos eigensolver for high-performance computers

NASA Technical Reports Server (NTRS)

Bostic, Susan W.

1990-01-01

The computational strategies used to implement a Lanczos-based-method eigensolver on the latest generation of supercomputers are described. Several examples of structural vibration and buckling problems are presented that show the effects of using optimization techniques to increase the vectorization of the computational steps. The data storage and access schemes and the tools and strategies that best exploit the computer resources are presented. The method is implemented on the Convex C220, the Cray 2, and the Cray Y-MP computers. Results show that very good computation rates are achieved for the most computationally intensive steps of the Lanczos algorithm and that the Lanczos algorithm is many times faster than other methods extensively used in the past.

A centre-free approach for resource allocation with lower bounds

NASA Astrophysics Data System (ADS)

Obando, Germán; Quijano, Nicanor; Rakoto-Ravalontsalama, Naly

2017-09-01

Since complexity and scale of systems are continuously increasing, there is a growing interest in developing distributed algorithms that are capable to address information constraints, specially for solving optimisation and decision-making problems. In this paper, we propose a novel method to solve distributed resource allocation problems that include lower bound constraints. The optimisation process is carried out by a set of agents that use a communication network to coordinate their decisions. Convergence and optimality of the method are guaranteed under some mild assumptions related to the convexity of the problem and the connectivity of the underlying graph. Finally, we compare our approach with other techniques reported in the literature, and we present some engineering applications.

Permanent Magnet Ecr Plasma Source With Magnetic Field Optimization

DOEpatents

Doughty, Frank C.; Spencer, John E.

2000-12-19

In a plasma-producing device, an optimized magnet field for electron cyclotron resonance plasma generation is provided by a shaped pole piece. The shaped pole piece adjusts spacing between the magnet and the resonance zone, creates a convex or concave resonance zone, and decreases stray fields between the resonance zone and the workpiece. For a cylindrical permanent magnet, the pole piece includes a disk adjacent the magnet together with an annular cylindrical sidewall structure axially aligned with the magnet and extending from the base around the permanent magnet. The pole piece directs magnetic field lines into the resonance zone, moving the resonance zone further from the face of the magnet. Additional permanent magnets or magnet arrays may be utilized to control field contours on a local scale. Rather than a permeable material, the sidewall structure may be composed of an annular cylindrical magnetic material having a polarity opposite that of the permanent magnet, creating convex regions in the resonance zone. An annular disk-shaped recurve section at the end of the sidewall structure forms magnetic mirrors keeping the plasma off the pole piece. A recurve section composed of magnetic material having a radial polarity forms convex regions and/or magnetic mirrors within the resonance zone.

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets

PubMed Central

Xiao, Xun; Geyer, Veikko F.; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F.

2016-01-01

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. PMID:27104582

Essays on the Economics of Climate Change, Biofuel and Food Prices

NASA Astrophysics Data System (ADS)

Seguin, Charles

Climate change is likely to be the most important global pollution problem that humanity has had to face so far. In this dissertation, I tackle issues directly and indirectly related to climate change, bringing my modest contribution to the body of human creativity trying to deal with climate change. First, I look at the impact of non-convex feedbacks on the optimal climate policy. Second, I try to derive the optimal biofuel policy acknowledging the potential negative impacts that biofuel production might have on food supply. Finally, I test empirically for the presence of loss aversion in food purchases, which might play a role in the consumer response to food price changes brought about by biofuel production. Non-convexities in feedback processes are increasingly found to be important in the climate system. To evaluate their impact on the optimal greenhouse gas (GHG) abate- ment policy, I introduce non-convex feedbacks in a stochastic pollution control model. I numerically calibrate the model to represent the mitigation of greenhouse gas (GHG) emissions contributing to global climate change. This approach makes two contributions to the literature. First, it develops a framework to tackle stochastic non-convex pollu- tion management problems. Second, it applies this framework to the problem of climate change. This approach is in contrast to most of the economic literature on climate change that focuses either on linear feedbacks or environmental thresholds. I find that non-convex feedbacks lead to a decision threshold in the optimal mitigation policy, and I characterize how this threshold depends on feedback parameters and stochasticity. There is great hope that biofuel can help reduce greenhouse gas emissions from fossil fuel. However, there are some concerns that biofuel would increase food prices. In an optimal control model, a co-author and I look at the optimal biofuel production when it competes for land with food production. In addition oil is not exhaustible and output is subject to climate change induced damages. We find that the competitive outcome does not necessarily yield an underproduction of biofuels, but when it does, second best policies like subsidies and mandates can improve welfare. In marketing, there has been extensive empirical research to ascertain whether there is evidence of loss aversion as predicted by several reference price preference theories. Most of that literature finds that there is indeed evidence of loss aversion for many different goods. I argue that it is possible that some of that evidence seemingly supporting loss aversion arises because price endogeneity is not properly taken into account. Using scanner data I study four product categories: bread, chicken, corn and tortilla chips, and pasta. Taking prices as exogenous, I find evidence of loss aversion for bread and corn and tortilla chips. However, when instrumenting prices, the "loss aversion evidence" disappears.

Living on the Edge: A Geometric Theory of Phase Transitions in Convex Optimization

DTIC Science & Technology

2013-03-24

framework for constructing a regularizer f that promotes a specified type of structure, as well as many additional examples. We say that the...Rd that promote the structures we expect to find in x0 8 D. AMELUNXEN, M. LOTZ, M. B. MCCOY, AND J. A. TROPP and y0. Then we can frame the convex...signal x0 is sparse in the standard basis, and the second signal U y0 is sparse in a known basis U . In this case, we can use `1 norms to promote

Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1982-12-21

and W. T. ZIEMBA (1981). Intro- duction to concave and generalized concave functions. In Gener- alized Concavity in Optimization and Economics (S...Schaible and W. T. Ziemba , eds.), pp. 21-50. Academic Press, New York. BANK, B., J. GUDDAT, D. KLATTE, B. KUMMER, and K. TAMMER (1982). Non- Linear

Policy-Relevant Nonconvexities in the Production of Multiple Forest Benefits?

Treesearch

Stephen K. Swallow; Peter J. Parks; David N. Wear

1990-01-01

This paper challenges common assumptions about convexity in forest rotation models which optimize timber plus nontimber benefits. If a local optimum occurs earlier than the globally optimal age, policy based on marginal incentives may achieve suboptimal results. Policy-relevant nonconvexities are more likely if (i) nontimber benefits dominate for young stands while...

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Clearance detector and method for motion and distance

DOEpatents

Xavier, Patrick G [Albuquerque, NM

2011-08-09

A method for correct and efficient detection of clearances between three-dimensional bodies in computer-based simulations, where one or both of the volumes is subject to translation and/or rotations. The method conservatively determines of the size of such clearances and whether there is a collision between the bodies. Given two bodies, each of which is undergoing separate motions, the method utilizes bounding-volume hierarchy representations for the two bodies and, mappings and inverse mappings for the motions of the two bodies. The method uses the representations, mappings and direction vectors to determine the directionally furthest locations of points on the convex hulls of the volumes virtually swept by the bodies and hence the clearance between the bodies, without having to calculate the convex hulls of the bodies. The method includes clearance detection for bodies comprising convex geometrical primitives and more specific techniques for bodies comprising convex polyhedra.

Adaptive convex combination approach for the identification of improper quaternion processes.

PubMed

Ujang, Bukhari Che; Jahanchahi, Cyrus; Took, Clive Cheong; Mandic, Danilo P

2014-01-01

Data-adaptive optimal modeling and identification of real-world vector sensor data is provided by combining the fractional tap-length (FT) approach with model order selection in the quaternion domain. To account rigorously for the generality of such processes, both second-order circular (proper) and noncircular (improper), the proposed approach in this paper combines the FT length optimization with both the strictly linear quaternion least mean square (QLMS) and widely linear QLMS (WL-QLMS). A collaborative approach based on QLMS and WL-QLMS is shown to both identify the type of processes (proper or improper) and to track their optimal parameters in real time. Analysis shows that monitoring the evolution of the convex mixing parameter within the collaborative approach allows us to track the improperness in real time. Further insight into the properties of those algorithms is provided by establishing a relationship between the steady-state error and optimal model order. The approach is supported by simulations on model order selection and identification of both strictly linear and widely linear quaternion-valued systems, such as those routinely used in renewable energy (wind) and human-centered computing (biomechanics).

Distortion outage minimization in Nakagami fading using limited feedback

NASA Astrophysics Data System (ADS)

Wang, Chih-Hong; Dey, Subhrakanti

2011-12-01

We focus on a decentralized estimation problem via a clustered wireless sensor network measuring a random Gaussian source where the clusterheads amplify and forward their received signals (from the intra-cluster sensors) over orthogonal independent stationary Nakagami fading channels to a remote fusion center that reconstructs an estimate of the original source. The objective of this paper is to design clusterhead transmit power allocation policies to minimize the distortion outage probability at the fusion center, subject to an expected sum transmit power constraint. In the case when full channel state information (CSI) is available at the clusterhead transmitters, the optimization problem can be shown to be convex and is solved exactly. When only rate-limited channel feedback is available, we design a number of computationally efficient sub-optimal power allocation algorithms to solve the associated non-convex optimization problem. We also derive an approximation for the diversity order of the distortion outage probability in the limit when the average transmission power goes to infinity. Numerical results illustrate that the sub-optimal power allocation algorithms perform very well and can close the outage probability gap between the constant power allocation (no CSI) and full CSI-based optimal power allocation with only 3-4 bits of channel feedback.

Sphenoid dysplasia in neurofibromatosis type 1: a new technique for repair.

PubMed

Concezio, Di Rocco; Amir, Samii; Gianpiero, Tamburrini; Luca, Massimi; Mario, Giordano

2017-06-01

Sphenoid bone dysplasia in neurofibromatosis type 1 is characterized by progressive exophthalmos and facial disfiguration secondary to herniation of meningeal and cerebral structures. We describe a technique for reconstruction of the sphenoid defect apt at preventing or correcting the ocular globe dislocation. After placement of spinal cerebrospinal fluid drainage to reduce intracranial pressure, the temporal pole is posteriorly dislocated extradurally. The greater sphenoid wing defect is identified. A titanium mesh covered by lyophilized dura, modeled in a curved fashion, is interposed between the bone defect and the cerebro-meningeal structures with its convex surface over the retracted temporal pole. The particular configuration of the titanium mesh allows a self-maintaining position due to the pressure exerted by the brain over its convex central part with its lateral margins consequently pushed and self-anchored against the medial and lateral walls of the temporal fossa. Screw fixation is not needed. The technique utilized in four cases proved to be reliable at the long-term clinical and neuroradiological controls (6 to 19 years). Sphenoid bone dysplasia in NF1, resulting in proptosis and exophthalmos, is usually progressive. It can be surgically repaired using a curved titanium mesh with the convexity faced to the temporal pole that is in the opposite fashion from all the techniques previously introduced. When utilized early in life, the technique can prevent the occurrence of the orbital and facial disfiguration.

Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem.

PubMed

Al-Mulhem, M; Al-Maghrabi, T

1998-01-01

This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions.

Determination of refractive index of a simple negative, positive, or zero power lens using wedged plated interferometer

NASA Technical Reports Server (NTRS)

Shukla, R. P.; Perera, G. M.; George, M. C.; Venkateswarlu, P.

1990-01-01

A nondestructive technique for measuring the refractive index of a negative lens using a wedged plate interferometer is described. The method can be also used for measuring the refractive index of convex or zero power lenses. Schematic diagrams are presented for the use of a wedged plate interferometer for measuring the refractive index of a concave lens and of a convex lens.

Direct single-layered fabrication of 3D concavo convex patterns in nano-stereolithography

NASA Astrophysics Data System (ADS)

Lim, T. W.; Park, S. H.; Yang, D. Y.; Kong, H. J.; Lee, K. S.

2006-09-01

A nano-surfacing process (NSP) is proposed to directly fabricate three-dimensional (3D) concavo convex-shaped microstructures such as micro-lens arrays using two-photon polymerization (TPP), a promising technique for fabricating arbitrary 3D highly functional micro-devices. In TPP, commonly utilized methods for fabricating complex 3D microstructures to date are based on a layer-by-layer accumulating technique employing two-dimensional sliced data derived from 3D computer-aided design data. As such, this approach requires much time and effort for precise fabrication. In this work, a novel single-layer exposure method is proposed in order to improve the fabricating efficiency for 3D concavo convex-shaped microstructures. In the NSP, 3D microstructures are divided into 13 sub-regions horizontally with consideration of the heights. Those sub-regions are then expressed as 13 characteristic colors, after which a multi-voxel matrix (MVM) is composed with the characteristic colors. Voxels with various heights and diameters are generated to construct 3D structures using a MVM scanning method. Some 3D concavo convex-shaped microstructures were fabricated to estimate the usefulness of the NSP, and the results show that it readily enables the fabrication of single-layered 3D microstructures.

Convergence of the Graph Allen-Cahn Scheme

NASA Astrophysics Data System (ADS)

Luo, Xiyang; Bertozzi, Andrea L.

2017-05-01

The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The diffuse interface model is widely used for modeling in material science, and can also be used as a proxy to total variation minimization. In Bertozzi and Flenner (Multiscale Model Simul 10(3):1090-1118, 2012), an algorithm was developed to generalize the diffuse interface model to graphs to solve the graph cut problem. This work analyzes the conditions for the graph diffuse interface algorithm to converge. Using techniques from numerical PDE and convex optimization, monotonicity in function value and convergence under an a posteriori condition are shown for a class of schemes under a graph-independent stepsize condition. We also generalize our results to incorporate spectral truncation, a common technique used to save computation cost, and also to the case of multiclass classification. Various numerical experiments are done to compare theoretical results with practical performance.

A Target-Less Vision-Based Displacement Sensor Based on Image Convex Hull Optimization for Measuring the Dynamic Response of Building Structures.

PubMed

Choi, Insub; Kim, JunHee; Kim, Donghyun

2016-12-08

Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called "TVDS") is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

PubMed Central

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-01-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. PMID:23271835

Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

NASA Astrophysics Data System (ADS)

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-11-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems.

PubMed

Telen, Dries; Van Riet, Nick; Logist, Flip; Van Impe, Jan

2015-06-01

Informative experiments are highly valuable for estimating parameters in nonlinear dynamic bioprocesses. Techniques for optimal experiment design ensure the systematic design of such informative experiments. The E-criterion which can be used as objective function in optimal experiment design requires the maximization of the smallest eigenvalue of the Fisher information matrix. However, one problem with the minimal eigenvalue function is that it can be nondifferentiable. In addition, no closed form expression exists for the computation of eigenvalues of a matrix larger than a 4 by 4 one. As eigenvalues are normally computed with iterative methods, state-of-the-art optimal control solvers are not able to exploit automatic differentiation to compute the derivatives with respect to the decision variables. In the current paper a reformulation strategy from the field of convex optimization is suggested to circumvent these difficulties. This reformulation requires the inclusion of a matrix inequality constraint involving positive semidefiniteness. In this paper, this positive semidefiniteness constraint is imposed via Sylverster's criterion. As a result the maximization of the minimum eigenvalue function can be formulated in standard optimal control solvers through the addition of nonlinear constraints. The presented methodology is successfully illustrated with a case study from the field of predictive microbiology. Copyright © 2015. Published by Elsevier Inc.

Graphical models for optimal power flow

DOE PAGES

Dvijotham, Krishnamurthy; Chertkov, Michael; Van Hentenryck, Pascal; ...

2016-09-13

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithmmore » for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.« less

Analysis, optimization, and implementation of a hybrid DS/FFH spread-spectrum technique for smart grid communications

DOE PAGES

Olama, Mohammed M.; Ma, Xiao; Killough, Stephen M.; ...

2015-03-12

In recent years, there has been great interest in using hybrid spread-spectrum (HSS) techniques for commercial applications, particularly in the Smart Grid, in addition to their inherent uses in military communications. This is because HSS can accommodate high data rates with high link integrity, even in the presence of significant multipath effects and interfering signals. A highly useful form of this transmission technique for many types of command, control, and sensing applications is the specific code-related combination of standard direct sequence modulation with fast frequency hopping, denoted hybrid DS/FFH, wherein multiple frequency hops occur within a single data-bit time. Inmore » this paper, error-probability analyses are performed for a hybrid DS/FFH system over standard Gaussian and fading-type channels, progressively including the effects from wide- and partial-band jamming, multi-user interference, and varying degrees of Rayleigh and Rician fading. In addition, an optimization approach is formulated that minimizes the bit-error performance of a hybrid DS/FFH communication system and solves for the resulting system design parameters. The optimization objective function is non-convex and can be solved by applying the Karush-Kuhn-Tucker conditions. We also present our efforts toward exploring the design, implementation, and evaluation of a hybrid DS/FFH radio transceiver using a single FPGA. Numerical and experimental results are presented under widely varying design parameters to demonstrate the adaptability of the waveform for varied harsh smart grid RF signal environments.« less

Image restoration by the method of convex projections: part 2 applications and numerical results.

PubMed

Sezan, M I; Stark, H

1982-01-01

The image restoration theory discussed in a previous paper by Youla and Webb [1] is applied to a simulated image and the results compared with the well-known method known as the Gerchberg-Papoulis algorithm. The results show that the method of image restoration by projection onto convex sets, by providing a convenient technique for utilizing a priori information, performs significantly better than the Gerchberg-Papoulis method.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining.

PubMed

Cheng, Wenlong; Zhao, Mingbo; Xiong, Naixue; Chui, Kwok Tai

2017-07-15

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l ₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating l p -norm and Schatten p -norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.

Efficient globally optimal segmentation of cells in fluorescence microscopy images using level sets and convex energy functionals.

PubMed

Bergeest, Jan-Philip; Rohr, Karl

2012-10-01

In high-throughput applications, accurate and efficient segmentation of cells in fluorescence microscopy images is of central importance for the quantification of protein expression and the understanding of cell function. We propose an approach for segmenting cell nuclei which is based on active contours using level sets and convex energy functionals. Compared to previous work, our approach determines the global solution. Thus, the approach does not suffer from local minima and the segmentation result does not depend on the initialization. We consider three different well-known energy functionals for active contour-based segmentation and introduce convex formulations of these functionals. We also suggest a numeric approach for efficiently computing the solution. The performance of our approach has been evaluated using fluorescence microscopy images from different experiments comprising different cell types. We have also performed a quantitative comparison with previous segmentation approaches. Copyright © 2012 Elsevier B.V. All rights reserved.

Explicit optimization of plan quality measures in intensity-modulated radiation therapy treatment planning.

PubMed

Engberg, Lovisa; Forsgren, Anders; Eriksson, Kjell; Hårdemark, Björn

2017-06-01

To formulate convex planning objectives of treatment plan multicriteria optimization with explicit relationships to the dose-volume histogram (DVH) statistics used in plan quality evaluation. Conventional planning objectives are designed to minimize the violation of DVH statistics thresholds using penalty functions. Although successful in guiding the DVH curve towards these thresholds, conventional planning objectives offer limited control of the individual points on the DVH curve (doses-at-volume) used to evaluate plan quality. In this study, we abandon the usual penalty-function framework and propose planning objectives that more closely relate to DVH statistics. The proposed planning objectives are based on mean-tail-dose, resulting in convex optimization. We also demonstrate how to adapt a standard optimization method to the proposed formulation in order to obtain a substantial reduction in computational cost. We investigated the potential of the proposed planning objectives as tools for optimizing DVH statistics through juxtaposition with the conventional planning objectives on two patient cases. Sets of treatment plans with differently balanced planning objectives were generated using either the proposed or the conventional approach. Dominance in the sense of better distributed doses-at-volume was observed in plans optimized within the proposed framework. The initial computational study indicates that the DVH statistics are better optimized and more efficiently balanced using the proposed planning objectives than using the conventional approach. © 2017 American Association of Physicists in Medicine.

Diagnostic performance of convex probe EBUS-TBNA in patients with mediastinal and coexistent endobronchial or peripheral lesions

PubMed Central

Verma, Akash; Goh, Kee San; Phua, Chee Kiang; Sim, Wen Yuan; Tee, Kuan Sen; Lim, Albert Y.H.; Tai, Dessmon Y.H.; Goh, Soon Keng; Kor, Ai Ching; Ho, Benjamin; Lew, Sennen J.W.; Abisheganaden, John

2016-01-01

Abstract To compare the performance of convex probe endobronchial ultrasound guided transbronchial needle aspiration (EBUS-TBNA) with conventional endobronchial biopsy (EBB) or transbronchial lung biopsy (TBLB) in patients with mediastinal, and coexisting endobronchial or peripheral lesions. Retrospective review of records of patients undergoing diagnostic EBUS-TBNA and conventional bronchoscopy in 2014. A total of 74 patients had mediastinal, and coexisting endobronchial or peripheral lesions. The detection rate of EBUS-TBNA for mediastinal lesion >1 cm in short axis, EBB for visible exophytic type of endobronchial lesion, and TBLB for peripheral lesion with bronchus sign were 71%, 75%, and 86%, respectively. In contrast, the detection rate of EBUS-TBNA for mediastinal lesion ≤1 cm in short axis, EBB for mucosal hyperemia type of endobronchial lesion, and TBLB for peripheral lesion without bronchus sign were 25%, 63%, and 38%, and improved to 63%, 88%, and 62% respectively by adding EBB or TBLB to EBUS-TBNA, and EBUS-TBNA to EBB or TBLB. Postprocedure bleeding was significantly more common in patients undergoing EBB and TBLB 8 (40%) versus convex probe EBUS-TBNA 2 patients (2.7%, P = 0.0004). EBUS-TBNA is a safer single diagnostic technique compared with EBB or TBLB in patients with mediastinal lesion of >1 cm in size, and coexisting exophytic type of endobronchial lesion, or peripheral lesion with bronchus sign. However, it requires combining with EBB or TBLB and vice versa to optimize yield when mediastinal lesion is ≤1 cm in size, and coexisting endobronchial and peripheral lesions lack exophytic nature, and bronchus sign, respectively. PMID:27977603

CometBoards Users Manual Release 1.0

NASA Technical Reports Server (NTRS)

Guptill, James D.; Coroneos, Rula M.; Patnaik, Surya N.; Hopkins, Dale A.; Berke, Lazlo

1996-01-01

Several nonlinear mathematical programming algorithms for structural design applications are available at present. These include the sequence of unconstrained minimizations technique, the method of feasible directions, and the sequential quadratic programming technique. The optimality criteria technique and the fully utilized design concept are two other structural design methods. A project was undertaken to bring all these design methods under a common computer environment so that a designer can select any one of these tools that may be suitable for his/her application. To facilitate selection of a design algorithm, to validate and check out the computer code, and to ascertain the relative merits of the design tools, modest finite element structural analysis programs based on the concept of stiffness and integrated force methods have been coupled to each design method. The code that contains both these design and analysis tools, by reading input information from analysis and design data files, can cast the design of a structure as a minimum-weight optimization problem. The code can then solve it with a user-specified optimization technique and a user-specified analysis method. This design code is called CometBoards, which is an acronym for Comparative Evaluation Test Bed of Optimization and Analysis Routines for the Design of Structures. This manual describes for the user a step-by-step procedure for setting up the input data files and executing CometBoards to solve a structural design problem. The manual includes the organization of CometBoards; instructions for preparing input data files; the procedure for submitting a problem; illustrative examples; and several demonstration problems. A set of 29 structural design problems have been solved by using all the optimization methods available in CometBoards. A summary of the optimum results obtained for these problems is appended to this users manual. CometBoards, at present, is available for Posix-based Cray and Convex computers, Iris and Sun workstations, and the VM/CMS system.

Detecting glaucomatous change in visual fields: Analysis with an optimization framework.

PubMed

Yousefi, Siamak; Goldbaum, Michael H; Varnousfaderani, Ehsan S; Belghith, Akram; Jung, Tzyy-Ping; Medeiros, Felipe A; Zangwill, Linda M; Weinreb, Robert N; Liebmann, Jeffrey M; Girkin, Christopher A; Bowd, Christopher

2015-12-01

Detecting glaucomatous progression is an important aspect of glaucoma management. The assessment of longitudinal series of visual fields, measured using Standard Automated Perimetry (SAP), is considered the reference standard for this effort. We seek efficient techniques for determining progression from longitudinal visual fields by formulating the problem as an optimization framework, learned from a population of glaucoma data. The longitudinal data from each patient's eye were used in a convex optimization framework to find a vector that is representative of the progression direction of the sample population, as a whole. Post-hoc analysis of longitudinal visual fields across the derived vector led to optimal progression (change) detection. The proposed method was compared to recently described progression detection methods and to linear regression of instrument-defined global indices, and showed slightly higher sensitivities at the highest specificities than other methods (a clinically desirable result). The proposed approach is simpler, faster, and more efficient for detecting glaucomatous changes, compared to our previously proposed machine learning-based methods, although it provides somewhat less information. This approach has potential application in glaucoma clinics for patient monitoring and in research centers for classification of study participants. Copyright © 2015 Elsevier Inc. All rights reserved.

Development of Analysis Tools for Certification of Flight Control Laws

DTIC Science & Technology

2009-03-31

In Proc. Conf. on Decision and Control, pages 881-886, Bahamas, 2004. [7] G. Chesi, A. Garulli, A. Tesi , and A. Vicino. LMI-based computation of...Minneapolis, MN, 2006, pp. 117-122. [10] G. Chesi, A. Garulli, A. Tesi . and A. Vicino, "LMI-based computation of optimal quadratic Lyapunov functions...Convex Optimization. Cambridge Univ. Press. Chesi, G., A. Garulli, A. Tesi and A. Vicino (2005). LMI-based computation of optimal quadratic Lyapunov

Comparison of baseline removal methods for laser-induced breakdown spectroscopy of geological samples

NASA Astrophysics Data System (ADS)

Dyar, M. Darby; Giguere, Stephen; Carey, CJ; Boucher, Thomas

2016-12-01

This project examines the causes, effects, and optimization of continuum removal in laser-induced breakdown spectroscopy (LIBS) to produce the best possible prediction accuracy of elemental composition in geological samples. We compare prediction accuracy resulting from several different techniques for baseline removal, including asymmetric least squares (ALS), adaptive iteratively reweighted penalized least squares (Air-PLS), fully automatic baseline correction (FABC), continuous wavelet transformation, median filtering, polynomial fitting, the iterative thresholding Dietrich method, convex hull/rubber band techniques, and a newly-developed technique for Custom baseline removal (BLR). We assess the predictive performance of these methods using partial least-squares analysis for 13 elements of geological interest, expressed as the weight percentages of SiO2, Al2O3, TiO2, FeO, MgO, CaO, Na2O, K2O, and the parts per million concentrations of Ni, Cr, Zn, Mn, and Co. We find that previously published methods for baseline subtraction generally produce equivalent prediction accuracies for major elements. When those pre-existing methods are used, automated optimization of their adjustable parameters is always necessary to wring the best predictive accuracy out of a data set; ideally, it should be done for each individual variable. The new technique of Custom BLR produces significant improvements in prediction accuracy over existing methods across varying geological data sets, instruments, and varying analytical conditions. These results also demonstrate the dual objectives of the continuum removal problem: removing a smooth underlying signal to fit individual peaks (univariate analysis) versus using feature selection to select only those channels that contribute to best prediction accuracy for multivariate analyses. Overall, the current practice of using generalized, one-method-fits-all-spectra baseline removal results in poorer predictive performance for all methods. The extra steps needed to optimize baseline removal for each predicted variable and empower multivariate techniques with the best possible input data for optimal prediction accuracy are shown to be well worth the slight increase in necessary computations and complexity.

Efficient Compressed Sensing Based MRI Reconstruction using Nonconvex Total Variation Penalties

NASA Astrophysics Data System (ADS)

Lazzaro, D.; Loli Piccolomini, E.; Zama, F.

2016-10-01

This work addresses the problem of Magnetic Resonance Image Reconstruction from highly sub-sampled measurements in the Fourier domain. It is modeled as a constrained minimization problem, where the objective function is a non-convex function of the gradient of the unknown image and the constraints are given by the data fidelity term. We propose an algorithm, Fast Non Convex Reweighted (FNCR), where the constrained problem is solved by a reweighting scheme, as a strategy to overcome the non-convexity of the objective function, with an adaptive adjustment of the penalization parameter. We propose a fast iterative algorithm and we can prove that it converges to a local minimum because the constrained problem satisfies the Kurdyka-Lojasiewicz property. Moreover the adaptation of non convex l0 approximation and penalization parameters, by means of a continuation technique, allows us to obtain good quality solutions, avoiding to get stuck in unwanted local minima. Some numerical experiments performed on MRI sub-sampled data show the efficiency of the algorithm and the accuracy of the solution.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

Geometric approach to segmentation and protein localization in cell culture assays.

PubMed

Raman, S; Maxwell, C A; Barcellos-Hoff, M H; Parvin, B

2007-01-01

Cell-based fluorescence imaging assays are heterogeneous and require the collection of a large number of images for detailed quantitative analysis. Complexities arise as a result of variation in spatial nonuniformity, shape, overlapping compartments and scale (size). A new technique and methodology has been developed and tested for delineating subcellular morphology and partitioning overlapping compartments at multiple scales. This system is packaged as an integrated software platform for quantifying images that are obtained through fluorescence microscopy. Proposed methods are model based, leveraging geometric shape properties of subcellular compartments and corresponding protein localization. From the morphological perspective, convexity constraint is imposed to delineate and partition nuclear compartments. From the protein localization perspective, radial symmetry is imposed to localize punctate protein events at submicron resolution. Convexity constraint is imposed against boundary information, which are extracted through a combination of zero-crossing and gradient operator. If the convexity constraint fails for the boundary then positive curvature maxima are localized along the contour and the entire blob is partitioned into disjointed convex objects representing individual nuclear compartment, by enforcing geometric constraints. Nuclear compartments provide the context for protein localization, which may be diffuse or punctate. Punctate signal are localized through iterative voting and radial symmetries for improved reliability and robustness. The technique has been tested against 196 images that were generated to study centrosome abnormalities. Corresponding computed representations are compared against manual counts for validation.

Final Technical Report: Sparse Grid Scenario Generation and Interior Algorithms for Stochastic Optimization in a Parallel Computing Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehrotra, Sanjay

2016-09-07

The support from this grant resulted in seven published papers and a technical report. Two papers are published in SIAM J. on Optimization [87, 88]; two papers are published in IEEE Transactions on Power Systems [77, 78]; one paper is published in Smart Grid [79]; one paper is published in Computational Optimization and Applications [44] and one in INFORMS J. on Computing [67]). The works in [44, 67, 87, 88] were funded primarily by this DOE grant. The applied papers in [77, 78, 79] were also supported through a subcontract from the Argonne National Lab. We start by presenting ourmore » main research results on the scenario generation problem in Sections 1–2. We present our algorithmic results on interior point methods for convex optimization problems in Section 3. We describe a new ‘central’ cutting surface algorithm developed for solving large scale convex programming problems (as is the case with our proposed research) with semi-infinite number of constraints in Section 4. In Sections 5–6 we present our work on two application problems of interest to DOE.« less

L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction.

PubMed

Zheng, Wenming; Lin, Zhouchen; Wang, Haixian

2014-04-01

A novel discriminant analysis criterion is derived in this paper under the theoretical framework of Bayes optimality. In contrast to the conventional Fisher's discriminant criterion, the major novelty of the proposed one is the use of L1 norm rather than L2 norm, which makes it less sensitive to the outliers. With the L1-norm discriminant criterion, we propose a new linear discriminant analysis (L1-LDA) method for linear feature extraction problem. To solve the L1-LDA optimization problem, we propose an efficient iterative algorithm, in which a novel surrogate convex function is introduced such that the optimization problem in each iteration is to simply solve a convex programming problem and a close-form solution is guaranteed to this problem. Moreover, we also generalize the L1-LDA method to deal with the nonlinear robust feature extraction problems via the use of kernel trick, and hereafter proposed the L1-norm kernel discriminant analysis (L1-KDA) method. Extensive experiments on simulated and real data sets are conducted to evaluate the effectiveness of the proposed method in comparing with the state-of-the-art methods.

Beam aperture modifier design with acoustic metasurfaces

NASA Astrophysics Data System (ADS)

Tang, Weipeng; Ren, Chunyu

2017-10-01

In this paper, we present a design concept of acoustic beam aperture modifier using two metasurface-based planar lenses. By appropriately designing the phase gradient profile along the metasurface, we obtain a class of acoustic convex lenses and concave lenses, which can focus the incoming plane waves and collimate the converging waves, respectively. On the basis of the high converging and diverging capability of these lenses, two kinds of lens combination scheme, including the convex-concave type and convex-convex type, are proposed to tune up the incoming beam aperture as needed. To be specific, the aperture of the acoustic beam can be shrunk or expanded through adjusting the phase gradient of the pair of lenses and the spacing between them. These lenses and the corresponding aperture modifiers are constructed by the stacking ultrathin labyrinthine structures, which are obtained by the geometry optimization procedure and exhibit high transmission coefficient and a full range of phase shift. The simulation results demonstrate the effectiveness of our proposed beam aperture modifiers. Due to the flexibility in aperture controlling and the simplicity in fabrication, the proposed modifiers have promising potential in applications, such as acoustic imaging, nondestructive evaluation, and communication.

Low-rank structure learning via nonconvex heuristic recovery.

PubMed

Deng, Yue; Dai, Qionghai; Liu, Risheng; Zhang, Zengke; Hu, Sanqing

2013-03-01

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

SU-D-BRA-04: Computerized Framework for Marker-Less Localization of Anatomical Feature Points in Range Images Based On Differential Geometry Features for Image-Guided Radiation Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soufi, M; Arimura, H; Toyofuku, F

Purpose: To propose a computerized framework for localization of anatomical feature points on the patient surface in infrared-ray based range images by using differential geometry (curvature) features. Methods: The general concept was to reconstruct the patient surface by using a mathematical modeling technique for the computation of differential geometry features that characterize the local shapes of the patient surfaces. A region of interest (ROI) was firstly extracted based on a template matching technique applied on amplitude (grayscale) images. The extracted ROI was preprocessed for reducing temporal and spatial noises by using Kalman and bilateral filters, respectively. Next, a smooth patientmore » surface was reconstructed by using a non-uniform rational basis spline (NURBS) model. Finally, differential geometry features, i.e. the shape index and curvedness features were computed for localizing the anatomical feature points. The proposed framework was trained for optimizing shape index and curvedness thresholds and tested on range images of an anthropomorphic head phantom. The range images were acquired by an infrared ray-based time-of-flight (TOF) camera. The localization accuracy was evaluated by measuring the mean of minimum Euclidean distances (MMED) between reference (ground truth) points and the feature points localized by the proposed framework. The evaluation was performed for points localized on convex regions (e.g. apex of nose) and concave regions (e.g. nasofacial sulcus). Results: The proposed framework has localized anatomical feature points on convex and concave anatomical landmarks with MMEDs of 1.91±0.50 mm and 3.70±0.92 mm, respectively. A statistically significant difference was obtained between the feature points on the convex and concave regions (P<0.001). Conclusion: Our study has shown the feasibility of differential geometry features for localization of anatomical feature points on the patient surface in range images. The proposed framework might be useful for tasks involving feature-based image registration in range-image guided radiation therapy.« less

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets.

PubMed

Xiao, Xun; Geyer, Veikko F; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F

2016-08-01

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Estimation of Saxophone Control Parameters by Convex Optimization.

PubMed

Wang, Cheng-I; Smyth, Tamara; Lipton, Zachary C

2014-12-01

In this work, an approach to jointly estimating the tone hole configuration (fingering) and reed model parameters of a saxophone is presented. The problem isn't one of merely estimating pitch as one applied fingering can be used to produce several different pitches by bugling or overblowing. Nor can a fingering be estimated solely by the spectral envelope of the produced sound (as it might for estimation of vocal tract shape in speech) since one fingering can produce markedly different spectral envelopes depending on the player's embouchure and control of the reed. The problem is therefore addressed by jointly estimating both the reed (source) parameters and the fingering (filter) of a saxophone model using convex optimization and 1) a bank of filter frequency responses derived from measurement of the saxophone configured with all possible fingerings and 2) sample recordings of notes produced using all possible fingerings, played with different overblowing, dynamics and timbre. The saxophone model couples one of several possible frequency response pairs (corresponding to the applied fingering), and a quasi-static reed model generating input pressure at the mouthpiece, with control parameters being blowing pressure and reed stiffness. Applied fingering and reed parameters are estimated for a given recording by formalizing a minimization problem, where the cost function is the error between the recording and the synthesized sound produced by the model having incremental parameter values for blowing pressure and reed stiffness. The minimization problem is nonlinear and not differentiable and is made solvable using convex optimization. The performance of the fingering identification is evaluated with better accuracy than previous reported value.

Hyperopt: a Python library for model selection and hyperparameter optimization

NASA Astrophysics Data System (ADS)

Bergstra, James; Komer, Brent; Eliasmith, Chris; Yamins, Dan; Cox, David D.

2015-01-01

Sequential model-based optimization (also known as Bayesian optimization) is one of the most efficient methods (per function evaluation) of function minimization. This efficiency makes it appropriate for optimizing the hyperparameters of machine learning algorithms that are slow to train. The Hyperopt library provides algorithms and parallelization infrastructure for performing hyperparameter optimization (model selection) in Python. This paper presents an introductory tutorial on the usage of the Hyperopt library, including the description of search spaces, minimization (in serial and parallel), and the analysis of the results collected in the course of minimization. This paper also gives an overview of Hyperopt-Sklearn, a software project that provides automatic algorithm configuration of the Scikit-learn machine learning library. Following Auto-Weka, we take the view that the choice of classifier and even the choice of preprocessing module can be taken together to represent a single large hyperparameter optimization problem. We use Hyperopt to define a search space that encompasses many standard components (e.g. SVM, RF, KNN, PCA, TFIDF) and common patterns of composing them together. We demonstrate, using search algorithms in Hyperopt and standard benchmarking data sets (MNIST, 20-newsgroups, convex shapes), that searching this space is practical and effective. In particular, we improve on best-known scores for the model space for both MNIST and convex shapes. The paper closes with some discussion of ongoing and future work.

Experimental Design for Estimating Unknown Hydraulic Conductivity in a Confined Aquifer using a Genetic Algorithm and a Reduced Order Model

NASA Astrophysics Data System (ADS)

Ushijima, T.; Yeh, W.

2013-12-01

An optimal experimental design algorithm is developed to select locations for a network of observation wells that provides the maximum information about unknown hydraulic conductivity in a confined, anisotropic aquifer. The design employs a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. Because that the formulated problem is non-convex and contains integer variables (necessitating a combinatorial search), for a realistically-scaled model, the problem may be difficult, if not impossible, to solve through traditional mathematical programming techniques. Genetic Algorithms (GAs) are designed to search out the global optimum; however because a GA requires a large number of calls to a groundwater model, the formulated optimization problem may still be infeasible to solve. To overcome this, Proper Orthogonal Decomposition (POD) is applied to the groundwater model to reduce its dimension. The information matrix in the full model space can then be searched without solving the full model.

A data driven control method for structure vibration suppression

NASA Astrophysics Data System (ADS)

Xie, Yangmin; Wang, Chao; Shi, Hang; Shi, Junwei

2018-02-01

High radio-frequency space applications have motivated continuous research on vibration suppression of large space structures both in academia and industry. This paper introduces a novel data driven control method to suppress vibrations of flexible structures and experimentally validates the suppression performance. Unlike model-based control approaches, the data driven control method designs a controller directly from the input-output test data of the structure, without requiring parametric dynamics and hence free of system modeling. It utilizes the discrete frequency response via spectral analysis technique and formulates a non-convex optimization problem to obtain optimized controller parameters with a predefined controller structure. Such approach is then experimentally applied on an end-driving flexible beam-mass structure. The experiment results show that the presented method can achieve competitive disturbance rejections compared to a model-based mixed sensitivity controller under the same design criterion but with much less orders and design efforts, demonstrating the proposed data driven control is an effective approach for vibration suppression of flexible structures.

Efficient 3D multi-region prostate MRI segmentation using dual optimization.

PubMed

Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron

2013-01-01

Efficient and accurate extraction of the prostate, in particular its clinically meaningful sub-regions from 3D MR images, is of great interest in image-guided prostate interventions and diagnosis of prostate cancer. In this work, we propose a novel multi-region segmentation approach to simultaneously locating the boundaries of the prostate and its two major sub-regions: the central gland and the peripheral zone. The proposed method utilizes the prior knowledge of the spatial region consistency and employs a customized prostate appearance model to simultaneously segment multiple clinically meaningful regions. We solve the resulted challenging combinatorial optimization problem by means of convex relaxation, for which we introduce a novel spatially continuous flow-maximization model and demonstrate its duality to the investigated convex relaxed optimization problem with the region consistency constraint. Moreover, the proposed continuous max-flow model naturally leads to a new and efficient continuous max-flow based algorithm, which enjoys great advantages in numerics and can be readily implemented on GPUs. Experiments using 15 T2-weighted 3D prostate MR images, by inter- and intra-operator variability, demonstrate the promising performance of the proposed approach.

Algorithms for Maneuvering Spacecraft Around Small Bodies

NASA Technical Reports Server (NTRS)

Acikmese, A. Bechet; Bayard, David

2006-01-01

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Estimation of positive semidefinite correlation matrices by using convex quadratic semidefinite programming.

PubMed

Fushiki, Tadayoshi

2009-07-01

The correlation matrix is a fundamental statistic that is used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used in the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume the approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.

Convex decomposition techniques applied to handlebodies

NASA Astrophysics Data System (ADS)

Ortiz, Marcos A.

Contact structures on 3-manifolds are 2-plane fields satisfying a set of conditions. The study of contact structures can be traced back for over two-hundred years, and has been of interest to mathematicians such as Hamilton, Jacobi, Cartan, and Darboux. In the late 1900's, the study of these structures gained momentum as the work of Eliashberg and Bennequin described subtleties in these structures that could be used to find new invariants. In particular, it was discovered that contact structures fell into two classes: tight and overtwisted. While overtwisted contact structures are relatively well understood, tight contact structures remain an area of active research. One area of active study, in particular, is the classification of tight contact structures on 3-manifolds. This began with Eliashberg, who showed that the standard contact structure in real three-dimensional space is unique, and it has been expanded on since. Some major advancements and new techniques were introduced by Kanda, Honda, Etnyre, Kazez, Matic, and others. Convex decomposition theory was one product of these explorations. This technique involves cutting a manifold along convex surfaces (i.e. surfaces arranged in a particular way in relation to the contact structure) and investigating a particular set on these cutting surfaces to say something about the original contact structure. In the cases where the cutting surfaces are fairly nice, in some sense, Honda established a correspondence between information on the cutting surfaces and the tight contact structures supported by the original manifold. In this thesis, convex surface theory is applied to the case of handlebodies with a restricted class of dividing sets. For some cases, classification is achieved, and for others, some interesting patterns arise and are investigated.

On the complexity of a combined homotopy interior method for convex programming

NASA Astrophysics Data System (ADS)

Yu, Bo; Xu, Qing; Feng, Guochen

2007-03-01

In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

A Duality Theory for Non-convex Problems in the Calculus of Variations

NASA Astrophysics Data System (ADS)

Bouchitté, Guy; Fragalà, Ilaria

2018-07-01

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).

A Duality Theory for Non-convex Problems in the Calculus of Variations

NASA Astrophysics Data System (ADS)

Bouchitté, Guy; Fragalà, Ilaria

2018-02-01

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).

Modeling IrisCode and its variants as convex polyhedral cones and its security implications.

PubMed

Kong, Adams Wai-Kin

2013-03-01

IrisCode, developed by Daugman, in 1993, is the most influential iris recognition algorithm. A thorough understanding of IrisCode is essential, because over 100 million persons have been enrolled by this algorithm and many biometric personal identification and template protection methods have been developed based on IrisCode. This paper indicates that a template produced by IrisCode or its variants is a convex polyhedral cone in a hyperspace. Its central ray, being a rough representation of the original biometric signal, can be computed by a simple algorithm, which can often be implemented in one Matlab command line. The central ray is an expected ray and also an optimal ray of an objective function on a group of distributions. This algorithm is derived from geometric properties of a convex polyhedral cone but does not rely on any prior knowledge (e.g., iris images). The experimental results show that biometric templates, including iris and palmprint templates, produced by different recognition methods can be matched through the central rays in their convex polyhedral cones and that templates protected by a method extended from IrisCode can be broken into. These experimental results indicate that, without a thorough security analysis, convex polyhedral cone templates cannot be assumed secure. Additionally, the simplicity of the algorithm implies that even junior hackers without knowledge of advanced image processing and biometric databases can still break into protected templates and reveal relationships among templates produced by different recognition methods.

Hodograph analysis in aircraft trajectory optimization

NASA Technical Reports Server (NTRS)

Cliff, Eugene M.; Seywald, Hans; Bless, Robert R.

1993-01-01

An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.

CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION.

PubMed

Wang, Lan; Kim, Yongdai; Li, Runze

2013-10-01

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis.

CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION

PubMed Central

Wang, Lan; Kim, Yongdai; Li, Runze

2014-01-01

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis. PMID:24948843

Structural optimization via a design space hierarchy

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.

1976-01-01

Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.

Algorithms for bilevel optimization

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

PubMed

Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen

2018-05-01

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli. We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Fabrication of large diffractive optical elements in thick film on a concave lens surface.

PubMed

Xie, Yongjun; Lu, Zhenwu; Li, Fengyou

2003-05-05

We demonstrate experimentally the technique of fabricating large diffractive optical elements (DOEs) in thick film on a concave lens surface (mirrors) with precise alignment by using the strategy of double exposure. We adopt the method of double exposure to overcome the difficulty of processing thick photoresist on a large curved substrate. A uniform thick film with arbitrary thickness on a concave lens can be obtained with this technique. We fabricate a large concentric circular grating with a 10-ìm period on a concave lens surface in film with a thickness of 2.0 ìm after development. It is believed that this technique can also be used to fabricate larger DOEs in thicker film on the concave or convex lens surface with precise alignment. There are other potential applications of this technique, such as fabrication of micro-optoelectromechanical systems (MOEMS) or microelectromechanical systems (MEMS) and fabrication of microlens arrays on a large concave lens surface or convex lens surface with precise alignment.

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

NASA Technical Reports Server (NTRS)

Blackmore, Lars

2008-01-01

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

Human performance on visually presented Traveling Salesman problems.

PubMed

Vickers, D; Butavicius, M; Lee, M; Medvedev, A

2001-01-01

Little research has been carried out on human performance in optimization problems, such as the Traveling Salesman problem (TSP). Studies by Polivanova (1974, Voprosy Psikhologii, 4, 41-51) and by MacGregor and Ormerod (1996, Perception & Psychophysics, 58, 527-539) suggest that: (1) the complexity of solutions to visually presented TSPs depends on the number of points on the convex hull; and (2) the perception of optimal structure is an innate tendency of the visual system, not subject to individual differences. Results are reported from two experiments. In the first, measures of the total length and completion speed of pathways, and a measure of path uncertainty were compared with optimal solutions produced by an elastic net algorithm and by several heuristic methods. Performance was also compared under instructions to draw the shortest or the most attractive pathway. In the second, various measures of performance were compared with scores on Raven's advanced progressive matrices (APM). The number of points on the convex hull did not determine the relative optimality of solutions, although both this factor and the total number of points influenced solution speed and path uncertainty. Subjects' solutions showed appreciable individual differences, which had a strong correlation with APM scores. The relation between perceptual organization and the process of solving visually presented TSPs is briefly discussed, as is the potential of optimization for providing a conceptual framework for the study of intelligence.

Eliciting Naturalistic Cortical Responses with a Sensory Prosthesis via Optimized Microstimulation

DTIC Science & Technology

2016-08-12

error and correlation as metrics amenable to highly efficient convex optimization. This study concentrates on characterizing the neural responses to both...spiking signal. For LFP, distance measures such as the traditional mean-squared error and cross- correlation can be used, whereas distances between spike...with parameters that describe their associated temporal dynamics and relations to the observed output. A description of the model follows, but we

Convex Hull Aided Registration Method (CHARM).

PubMed

Fan, Jingfan; Yang, Jian; Zhao, Yitian; Ai, Danni; Liu, Yonghuai; Wang, Ge; Wang, Yongtian

2017-09-01

Non-rigid registration finds many applications such as photogrammetry, motion tracking, model retrieval, and object recognition. In this paper we propose a novel convex hull aided registration method (CHARM) to match two point sets subject to a non-rigid transformation. First, two convex hulls are extracted from the source and target respectively. Then, all points of the point sets are projected onto the reference plane through each triangular facet of the hulls. From these projections, invariant features are extracted and matched optimally. The matched feature point pairs are mapped back onto the triangular facets of the convex hulls to remove outliers that are outside any relevant triangular facet. The rigid transformation from the source to the target is robustly estimated by the random sample consensus (RANSAC) scheme through minimizing the distance between the matched feature point pairs. Finally, these feature points are utilized as the control points to achieve non-rigid deformation in the form of thin-plate spline of the entire source point set towards the target one. The experimental results based on both synthetic and real data show that the proposed algorithm outperforms several state-of-the-art ones with respect to sampling, rotational angle, and data noise. In addition, the proposed CHARM algorithm also shows higher computational efficiency compared to these methods.

Scalable Metropolis Monte Carlo for simulation of hard shapes

NASA Astrophysics Data System (ADS)

Anderson, Joshua A.; Eric Irrgang, M.; Glotzer, Sharon C.

2016-07-01

We design and implement a scalable hard particle Monte Carlo simulation toolkit (HPMC), and release it open source as part of HOOMD-blue. HPMC runs in parallel on many CPUs and many GPUs using domain decomposition. We employ BVH trees instead of cell lists on the CPU for fast performance, especially with large particle size disparity, and optimize inner loops with SIMD vector intrinsics on the CPU. Our GPU kernel proposes many trial moves in parallel on a checkerboard and uses a block-level queue to redistribute work among threads and avoid divergence. HPMC supports a wide variety of shape classes, including spheres/disks, unions of spheres, convex polygons, convex spheropolygons, concave polygons, ellipsoids/ellipses, convex polyhedra, convex spheropolyhedra, spheres cut by planes, and concave polyhedra. NVT and NPT ensembles can be run in 2D or 3D triclinic boxes. Additional integration schemes permit Frenkel-Ladd free energy computations and implicit depletant simulations. In a benchmark system of a fluid of 4096 pentagons, HPMC performs 10 million sweeps in 10 min on 96 CPU cores on XSEDE Comet. The same simulation would take 7.6 h in serial. HPMC also scales to large system sizes, and the same benchmark with 16.8 million particles runs in 1.4 h on 2048 GPUs on OLCF Titan.

A Fourier dimensionality reduction model for big data interferometric imaging

NASA Astrophysics Data System (ADS)

Vijay Kartik, S.; Carrillo, Rafael E.; Thiran, Jean-Philippe; Wiaux, Yves

2017-06-01

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the independent and identically distributed Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard ℓ2-norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work. matlab code implementing the proposed reduction method is available on GitHub.

A formulation of a matrix sparsity approach for the quantum ordered search algorithm

NASA Astrophysics Data System (ADS)

Parmar, Jupinder; Rahman, Saarim; Thiara, Jaskaran

One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database. Classically, the optimal algorithm is known to have a log2N complexity; however, Grovers algorithm has been found to have an optimal complexity between the lower bound of ((lnN-1)/π≈0.221log2N) and the upper bound of 0.433log2N. We sought to lower the known upper bound of the OSP. With Farhi et al. MITCTP 2815 (1999), arXiv:quant-ph/9901059], we see that the OSP can be resolved into a translational invariant algorithm to create quantum query algorithm restraints. With these restraints, one can find Laurent polynomials for various k — queries — and N — database sizes — thus finding larger recursive sets to solve the OSP and effectively reducing the upper bound. These polynomials are found to be convex functions, allowing one to make use of convex optimization to find an improvement on the known bounds. According to Childs et al. [Phys. Rev. A 75 (2007) 032335], semidefinite programming, a subset of convex optimization, can solve the particular problem represented by the constraints. We were able to implement a program abiding to their formulation of a semidefinite program (SDP), leading us to find that it takes an immense amount of storage and time to compute. To combat this setback, we then formulated an approach to improve results of the SDP using matrix sparsity. Through the development of this approach, along with an implementation of a rudimentary solver, we demonstrate how matrix sparsity reduces the amount of time and storage required to compute the SDP — overall ensuring further improvements will likely be made to reach the theorized lower bound.

Spatiotemporal radiotherapy planning using a global optimization approach

NASA Astrophysics Data System (ADS)

Adibi, Ali; Salari, Ehsan

2018-02-01

This paper aims at quantifying the extent of potential therapeutic gain, measured using biologically effective dose (BED), that can be achieved by altering the radiation dose distribution over treatment sessions in fractionated radiotherapy. To that end, a spatiotemporally integrated planning approach is developed, where the spatial and temporal dose modulations are optimized simultaneously. The concept of equivalent uniform BED (EUBED) is used to quantify and compare the clinical quality of spatiotemporally heterogeneous dose distributions in target and critical structures. This gives rise to a large-scale non-convex treatment-plan optimization problem, which is solved using global optimization techniques. The proposed spatiotemporal planning approach is tested on two stylized cancer cases resembling two different tumor sites and sensitivity analysis is performed for radio-biological and EUBED parameters. Numerical results validate that spatiotemporal plans are capable of delivering a larger BED to the target volume without increasing the BED in critical structures compared to conventional time-invariant plans. In particular, this additional gain is attributed to the irradiation of different regions of the target volume at different treatment sessions. Additionally, the trade-off between the potential therapeutic gain and the number of distinct dose distributions is quantified, which suggests a diminishing marginal gain as the number of dose distributions increases.

Fast approximate delivery of fluence maps for IMRT and VMAT

NASA Astrophysics Data System (ADS)

Balvert, Marleen; Craft, David

2017-02-01

In this article we provide a method to generate the trade-off between delivery time and fluence map matching quality for dynamically delivered fluence maps. At the heart of our method lies a mathematical programming model that, for a given duration of delivery, optimizes leaf trajectories and dose rates such that the desired fluence map is reproduced as well as possible. We begin with the single fluence map case and then generalize the model and the solution technique to the delivery of sequential fluence maps. The resulting large-scale, non-convex optimization problem was solved using a heuristic approach. We test our method using a prostate case and a head and neck case, and present the resulting trade-off curves. Analysis of the leaf trajectories reveals that short time plans have larger leaf openings in general than longer delivery time plans. Our method allows one to explore the continuum of possibilities between coarse, large segment plans characteristic of direct aperture approaches and narrow field plans produced by sliding window approaches. Exposing this trade-off will allow for an informed choice between plan quality and solution time. Further research is required to speed up the optimization process to make this method clinically implementable.

Holistic irrigation water management approach based on stochastic soil water dynamics

NASA Astrophysics Data System (ADS)

Alizadeh, H.; Mousavi, S. J.

2012-04-01

Appreciating the essential gap between fundamental unsaturated zone transport processes and soil and water management due to low effectiveness of some of monitoring and modeling approaches, this study presents a mathematical programming model for irrigation management optimization based on stochastic soil water dynamics. The model is a nonlinear non-convex program with an economic objective function to address water productivity and profitability aspects in irrigation management through optimizing irrigation policy. Utilizing an optimization-simulation method, the model includes an eco-hydrological integrated simulation model consisting of an explicit stochastic module of soil moisture dynamics in the crop-root zone with shallow water table effects, a conceptual root-zone salt balance module, and the FAO crop yield module. Interdependent hydrology of soil unsaturated and saturated zones is treated in a semi-analytical approach in two steps. At first step analytical expressions are derived for the expected values of crop yield, total water requirement and soil water balance components assuming fixed level for shallow water table, while numerical Newton-Raphson procedure is employed at the second step to modify value of shallow water table level. Particle Swarm Optimization (PSO) algorithm, combined with the eco-hydrological simulation model, has been used to solve the non-convex program. Benefiting from semi-analytical framework of the simulation model, the optimization-simulation method with significantly better computational performance compared to a numerical Mote-Carlo simulation-based technique has led to an effective irrigation management tool that can contribute to bridging the gap between vadose zone theory and water management practice. In addition to precisely assessing the most influential processes at a growing season time scale, one can use the developed model in large scale systems such as irrigation districts and agricultural catchments. Accordingly, the model has been applied in Dasht-e-Abbas and Ein-khosh Fakkeh Irrigation Districts (DAID and EFID) of the Karkheh Basin in southwest of Iran. The area suffers from the water scarcity problem and therefore the trade-off between the level of deficit and economical profit should be assessed. Based on the results, while the maximum net benefit has been obtained for the stress-avoidance (SA) irrigation policy, the highest water profitability, defined by economical net benefit gained from unit irrigation water volume application, has been resulted when only about 60% of water used in the SA policy is applied.

Footstep Planning on Uneven Terrain with Mixed-Integer Convex Optimization

DTIC Science & Technology

2014-08-01

ORGANIZATION NAME(S) AND ADDRESS(ES) Massachusetts Institute of Technology,Computer Science and Artificial Intellegence Laboratory,Cambridge,MA,02139...the MIT Energy Initiative, MIT CSAIL, and the DARPA Robotics Challenge. 1Robin Deits is with the Computer Science and Artificial Intelligence Laboratory

Cygnus A super-resolved via convex optimization from VLA data

NASA Astrophysics Data System (ADS)

Dabbech, A.; Onose, A.; Abdulaziz, A.; Perley, R. A.; Smirnov, O. M.; Wiaux, Y.

2018-05-01

We leverage the Sparsity Averaging Re-weighted Analysis approach for interferometric imaging, that is based on convex optimization, for the super-resolution of Cyg A from observations at the frequencies 8.422 and 6.678 GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned primal-dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional CLEAN-based methods, reflected in super-resolved images with high fidelity. The high-resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324 and 14.252 GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our MATLAB code is available online on GitHub.

Detection of faults in rotating machinery using periodic time-frequency sparsity

NASA Astrophysics Data System (ADS)

Ding, Yin; He, Wangpeng; Chen, Binqiang; Zi, Yanyang; Selesnick, Ivan W.

2016-11-01

This paper addresses the problem of extracting periodic oscillatory features in vibration signals for detecting faults in rotating machinery. To extract the feature, we propose an approach in the short-time Fourier transform (STFT) domain where the periodic oscillatory feature manifests itself as a relatively sparse grid. To estimate the sparse grid, we formulate an optimization problem using customized binary weights in the regularizer, where the weights are formulated to promote periodicity. In order to solve the proposed optimization problem, we develop an algorithm called augmented Lagrangian majorization-minimization algorithm, which combines the split augmented Lagrangian shrinkage algorithm (SALSA) with majorization-minimization (MM), and is guaranteed to converge for both convex and non-convex formulation. As examples, the proposed approach is applied to simulated data, and used as a tool for diagnosing faults in bearings and gearboxes for real data, and compared to some state-of-the-art methods. The results show that the proposed approach can effectively detect and extract the periodical oscillatory features.

Scalable analysis of nonlinear systems using convex optimization

NASA Astrophysics Data System (ADS)

Papachristodoulou, Antonis

In this thesis, we investigate how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically. The methodology is based on the construction of appropriate Lyapunov-type certificates using sum of squares techniques. After a brief introduction on the mathematical tools that we will be using, we turn our attention to robust stability and performance analysis of systems described by Ordinary Differential Equations. A general framework for constrained systems analysis is developed, under which stability of systems with polynomial, non-polynomial vector fields and switching systems, as well estimating the region of attraction and the L2 gain can be treated in a unified manner. We apply our results to examples from biology and aerospace. We then consider systems described by Functional Differential Equations (FDEs), i.e., time-delay systems. Their main characteristic is that they are infinite dimensional, which complicates their analysis. We first show how the complete Lyapunov-Krasovskii functional can be constructed algorithmically for linear time-delay systems. Then, we concentrate on delay-independent and delay-dependent stability analysis of nonlinear FDEs using sum of squares techniques. An example from ecology is given. The scalable stability analysis of congestion control algorithms for the Internet is investigated next. The models we use result in an arbitrary interconnection of FDE subsystems, for which we require that stability holds for arbitrary delays, network topologies and link capacities. Through a constructive proof, we develop a Lyapunov functional for FAST---a recently developed network congestion control scheme---so that the Lyapunov stability properties scale with the system size. We also show how other network congestion control schemes can be analyzed in the same way. Finally, we concentrate on systems described by Partial Differential Equations. We show that axially constant perturbations of the Navier-Stokes equations for Hagen-Poiseuille flow are globally stable, even though the background noise is amplified as R3 where R is the Reynolds number, giving a 'robust yet fragile' interpretation. We also propose a sum of squares methodology for the analysis of systems described by parabolic PDEs. We conclude this work with an account for future research.

Neural network for solving convex quadratic bilevel programming problems.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

Method and system for diagnostics of apparatus

NASA Technical Reports Server (NTRS)

Gorinevsky, Dimitry (Inventor)

2012-01-01

Proposed is a method, implemented in software, for estimating fault state of an apparatus outfitted with sensors. At each execution period the method processes sensor data from the apparatus to obtain a set of parity parameters, which are further used for estimating fault state. The estimation method formulates a convex optimization problem for each fault hypothesis and employs a convex solver to compute fault parameter estimates and fault likelihoods for each fault hypothesis. The highest likelihoods and corresponding parameter estimates are transmitted to a display device or an automated decision and control system. The obtained accurate estimate of fault state can be used to improve safety, performance, or maintenance processes for the apparatus.

Optimizer convergence and local minima errors and their clinical importance

NASA Astrophysics Data System (ADS)

Jeraj, Robert; Wu, Chuan; Mackie, Thomas R.

2003-09-01

Two of the errors common in the inverse treatment planning optimization have been investigated. The first error is the optimizer convergence error, which appears because of non-perfect convergence to the global or local solution, usually caused by a non-zero stopping criterion. The second error is the local minima error, which occurs when the objective function is not convex and/or the feasible solution space is not convex. The magnitude of the errors, their relative importance in comparison to other errors as well as their clinical significance in terms of tumour control probability (TCP) and normal tissue complication probability (NTCP) were investigated. Two inherently different optimizers, a stochastic simulated annealing and deterministic gradient method were compared on a clinical example. It was found that for typical optimization the optimizer convergence errors are rather small, especially compared to other convergence errors, e.g., convergence errors due to inaccuracy of the current dose calculation algorithms. This indicates that stopping criteria could often be relaxed leading into optimization speed-ups. The local minima errors were also found to be relatively small and typically in the range of the dose calculation convergence errors. Even for the cases where significantly higher objective function scores were obtained the local minima errors were not significantly higher. Clinical evaluation of the optimizer convergence error showed good correlation between the convergence of the clinical TCP or NTCP measures and convergence of the physical dose distribution. On the other hand, the local minima errors resulted in significantly different TCP or NTCP values (up to a factor of 2) indicating clinical importance of the local minima produced by physical optimization.

Optimizer convergence and local minima errors and their clinical importance.

PubMed

Jeraj, Robert; Wu, Chuan; Mackie, Thomas R

2003-09-07

Two of the errors common in the inverse treatment planning optimization have been investigated. The first error is the optimizer convergence error, which appears because of non-perfect convergence to the global or local solution, usually caused by a non-zero stopping criterion. The second error is the local minima error, which occurs when the objective function is not convex and/or the feasible solution space is not convex. The magnitude of the errors, their relative importance in comparison to other errors as well as their clinical significance in terms of tumour control probability (TCP) and normal tissue complication probability (NTCP) were investigated. Two inherently different optimizers, a stochastic simulated annealing and deterministic gradient method were compared on a clinical example. It was found that for typical optimization the optimizer convergence errors are rather small, especially compared to other convergence errors, e.g., convergence errors due to inaccuracy of the current dose calculation algorithms. This indicates that stopping criteria could often be relaxed leading into optimization speed-ups. The local minima errors were also found to be relatively small and typically in the range of the dose calculation convergence errors. Even for the cases where significantly higher objective function scores were obtained the local minima errors were not significantly higher. Clinical evaluation of the optimizer convergence error showed good correlation between the convergence of the clinical TCP or NTCP measures and convergence of the physical dose distribution. On the other hand, the local minima errors resulted in significantly different TCP or NTCP values (up to a factor of 2) indicating clinical importance of the local minima produced by physical optimization.

Coordinated control of active and reactive power of distribution network with distributed PV cluster via model predictive control

NASA Astrophysics Data System (ADS)

Ji, Yu; Sheng, Wanxing; Jin, Wei; Wu, Ming; Liu, Haitao; Chen, Feng

2018-02-01

A coordinated optimal control method of active and reactive power of distribution network with distributed PV cluster based on model predictive control is proposed in this paper. The method divides the control process into long-time scale optimal control and short-time scale optimal control with multi-step optimization. The models are transformed into a second-order cone programming problem due to the non-convex and nonlinear of the optimal models which are hard to be solved. An improved IEEE 33-bus distribution network system is used to analyse the feasibility and the effectiveness of the proposed control method

Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

PubMed

Wang, Xinghu; Hong, Yiguang; Ji, Haibo

2016-07-01

The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

Optimization-based mesh correction with volume and convexity constraints

DOE PAGES

D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; ...

2016-02-24

In this study, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimizationmore » problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.« less

Planning minimum-energy paths in an off-road environment with anisotropic traversal costs and motion constraints. Doctoral thesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ross, R.S.

1989-06-01

For a vehicle operating across arbitrarily-contoured terrain, finding the most fuel-efficient route between two points can be viewed as a high-level global path-planning problem with traversal costs and stability dependent on the direction of travel (anisotropic). The problem assumes a two-dimensional polygonal map of homogeneous cost regions for terrain representation constructed from elevation information. The anisotropic energy cost of vehicle motion has a non-braking component dependent on horizontal distance, a braking component dependent on vertical distance, and a constant path-independent component. The behavior of minimum-energy paths is then proved to be restricted to a small, but optimal set of traversalmore » types. An optimal-path-planning algorithm, using a heuristic search technique, reduces the infinite number of paths between the start and goal points to a finite number by generating sequences of goal-feasible window lists from analyzing the polygonal map and applying pruning criteria. The pruning criteria consist of visibility analysis, heading analysis, and region-boundary constraints. Each goal-feasible window lists specifies an associated convex optimization problem, and the best of all locally-optimal paths through the goal-feasible window lists is the globally-optimal path. These ideas have been implemented in a computer program, with results showing considerably better performance than the exponential average-case behavior predicted.« less

Blind Compressed Image Watermarking for Noisy Communication Channels

DTIC Science & Technology

2015-10-26

Lenna test image [11] for our simulations, and gradient projection for sparse recon- struction (GPSR) [12] to solve the convex optimization prob- lem...E. Candes, J. Romberg , and T. Tao, “Robust uncertainty prin- ciples: exact signal reconstruction from highly incomplete fre- quency information,” IEEE...Images - Requirements and Guidelines,” ITU-T Recommen- dation T.81, 1992. [6] M. Gkizeli, D. Pados, and M. Medley, “Optimal signature de - sign for

H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

PubMed

Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

2018-03-01

This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Stabilization for sampled-data neural-network-based control systems.

PubMed

Zhu, Xun-Lin; Wang, Youyi

2011-02-01

This paper studies the problem of stabilization for sampled-data neural-network-based control systems with an optimal guaranteed cost. Unlike previous works, the resulting closed-loop system with variable uncertain sampling cannot simply be regarded as an ordinary continuous-time system with a fast-varying delay in the state. By defining a novel piecewise Lyapunov functional and using a convex combination technique, the characteristic of sampled-data systems is captured. A new delay-dependent stabilization criterion is established in terms of linear matrix inequalities such that the maximal sampling interval and the minimal guaranteed cost control performance can be obtained. It is shown that the newly proposed approach can lead to less conservative and less complex results than the existing ones. Application examples are given to illustrate the effectiveness and the benefits of the proposed method.

Stochastic search, optimization and regression with energy applications

NASA Astrophysics Data System (ADS)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings. Finally, we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel-based weights and Dirichlet process-based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour-ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

Improving the growth of CZT crystals for radiation detectors: a modeling perspective

NASA Astrophysics Data System (ADS)

Derby, Jeffrey J.; Zhang, Nan; Yeckel, Andrew

2012-10-01

The availability of large, single crystals of cadmium zinc telluride (CZT) with uniform properties is key to improving the performance of gamma radiation detectors fabricated from them. Towards this goal, we discuss results obtained by computational models that provide a deeper understanding of crystal growth processes and how the growth of CZT can be improved. In particular, we discuss methods that may be implemented to lessen the deleterious interactions between the ampoule wall and the growing crystal via engineering a convex solidification interface. For vertical Bridgman growth, a novel, bell-curve furnace temperature profile is predicted to achieve macroscopically convex solid-liquid interface shapes during melt growth of CZT in a multiple-zone furnace. This approach represents a significant advance over traditional gradient-freeze profiles, which always yield concave interface shapes, and static heat transfer designs, such as pedestal design, that achieve convex interfaces over only a small portion of the growth run. Importantly, this strategy may be applied to any Bridgman configuration that utilizes multiple, controllable heating zones. Realizing a convex solidification interface via this adaptive bell-curve furnace profile is postulated to result in better crystallinity and higher yields than conventional CZT growth techniques.

Generalized ensemble method applied to study systems with strong first order transitions

DOE PAGES

Malolepsza, E.; Kim, J.; Keyes, T.

2015-09-28

At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub, where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM).more » This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. Lastly, the method is illustrated in a study of the very strong solid/liquid transition in water.« less

On base station cooperation using statistical CSI in jointly correlated MIMO downlink channels

NASA Astrophysics Data System (ADS)

Zhang, Jun; Jiang, Bin; Jin, Shi; Gao, Xiqi; Wong, Kai-Kit

2012-12-01

This article studies the transmission of a single cell-edge user's signal using statistical channel state information at cooperative base stations (BSs) with a general jointly correlated multiple-input multiple-output (MIMO) channel model. We first present an optimal scheme to maximize the ergodic sum capacity with per-BS power constraints, revealing that the transmitted signals of all BSs are mutually independent and the optimum transmit directions for each BS align with the eigenvectors of the BS's own transmit correlation matrix of the channel. Then, we employ matrix permanents to derive a closed-form tight upper bound for the ergodic sum capacity. Based on these results, we develop a low-complexity power allocation solution using convex optimization techniques and a simple iterative water-filling algorithm (IWFA) for power allocation. Finally, we derive a necessary and sufficient condition for which a beamforming approach achieves capacity for all BSs. Simulation results demonstrate that the upper bound of ergodic sum capacity is tight and the proposed cooperative transmission scheme increases the downlink system sum capacity considerably.

Sum-of-Squares-Based Region of Attraction Analysis for Gain-Scheduled Three-Loop Autopilot

NASA Astrophysics Data System (ADS)

Seo, Min-Won; Kwon, Hyuck-Hoon; Choi, Han-Lim

2018-04-01

A conventional method of designing a missile autopilot is to linearize the original nonlinear dynamics at several trim points, then to determine linear controllers for each linearized model, and finally implement gain-scheduling technique. The validation of such a controller is often based on linear system analysis for the linear closed-loop system at the trim conditions. Although this type of gain-scheduled linear autopilot works well in practice, validation based solely on linear analysis may not be sufficient to fully characterize the closed-loop system especially when the aerodynamic coefficients exhibit substantial nonlinearity with respect to the flight condition. The purpose of this paper is to present a methodology for analyzing the stability of a gain-scheduled controller in a setting close to the original nonlinear setting. The method is based on sum-of-squares (SOS) optimization that can be used to characterize the region of attraction of a polynomial system by solving convex optimization problems. The applicability of the proposed SOS-based methodology is verified on a short-period autopilot of a skid-to-turn missile.

Differentiable McCormick relaxations

DOE PAGES

Khan, Kamil A.; Watson, Harry A. J.; Barton, Paul I.

2016-05-27

McCormick's classical relaxation technique constructs closed-form convex and concave relaxations of compositions of simple intrinsic functions. These relaxations have several properties which make them useful for lower bounding problems in global optimization: they can be evaluated automatically, accurately, and computationally inexpensively, and they converge rapidly to the relaxed function as the underlying domain is reduced in size. They may also be adapted to yield relaxations of certain implicit functions and differential equation solutions. However, McCormick's relaxations may be nonsmooth, and this nonsmoothness can create theoretical and computational obstacles when relaxations are to be deployed. This article presents a continuously differentiablemore » variant of McCormick's original relaxations in the multivariate McCormick framework of Tsoukalas and Mitsos. Gradients of the new differentiable relaxations may be computed efficiently using the standard forward or reverse modes of automatic differentiation. Furthermore, extensions to differentiable relaxations of implicit functions and solutions of parametric ordinary differential equations are discussed. A C++ implementation based on the library MC++ is described and applied to a case study in nonsmooth nonconvex optimization.« less

Generalized ensemble method applied to study systems with strong first order transitions

NASA Astrophysics Data System (ADS)

Małolepsza, E.; Kim, J.; Keyes, T.

2015-09-01

At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub [1], where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM). This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. The method is illustrated in a study of the very strong solid/liquid transition in water.

Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; den Hertog, Dick; Siem, Alex Y. D.; Kaanders, Johannes H. A. M.; Huizenga, Henk

2008-11-01

Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier.

Surface tension effects on fully developed liquid layer flow over a convex corner

NASA Astrophysics Data System (ADS)

Bhatti, Ifrah; Farid, Saadia; Ullah, Saif; Riaz, Samia; Faryad, Maimoona

2018-04-01

This investigation deals with the study of fully developed liquid layer flow along with surface tension effects, confronting a convex corner in the direction of fluid flow. At the point of interaction, the related equations are formulated using double deck structure and match asymptotic techniques. Linearized solutions for small angle are obtained analytically. The solutions corresponding to similar flow neglecting surface tension effects are also recovered as special case of our general solutions. Finally, the influence of pertinent parameters on the flow, as well as a comparison between models, are shown by graphical illustration.

Ray Tracing with Virtual Objects.

ERIC Educational Resources Information Center

Leinoff, Stuart

1991-01-01

Introduces the method of ray tracing to analyze the refraction or reflection of real or virtual images from multiple optical devices. Discusses ray-tracing techniques for locating images using convex and concave lenses or mirrors. (MDH)

Ion beam figuring of Φ520mm convex hyperbolic secondary mirror

NASA Astrophysics Data System (ADS)

Meng, Xiaohui; Wang, Yonggang; Li, Ang; Li, Wenqing

2016-10-01

The convex hyperbolic secondary mirror is a Φ520-mm Zerodur lightweight hyperbolic convex mirror. Typically conventional methods like CCOS, stressed-lap polishing are used to manufacture this secondary mirror. Nevertheless, the required surface accuracy cannot be achieved through the use of conventional polishing methods because of the unpredictable behavior of the polishing tools, which leads to an unstable removal rate. Ion beam figuring is an optical fabrication method that provides highly controlled error of previously polished surfaces using a directed, inert and neutralized ion beam to physically sputter material from the optic surface. Several iterations with different ion beam size are selected and optimized to fit different stages of surface figure error and spatial frequency components. Before ion beam figuring, surface figure error of the secondary mirror is 2.5λ p-v, 0.23λ rms, and is improved to 0.12λ p-v, 0.014λ rms in several process iterations. The demonstration clearly shows that ion beam figuring can not only be used to the final correction of aspheric, but also be suitable for polishing the coarse surface of large, complex mirror.

A Fuzzy Approach of the Competition on the Air Transport Market

NASA Technical Reports Server (NTRS)

Charfeddine, Souhir; DeColigny, Marc; Camino, Felix Mora; Cosenza, Carlos Alberto Nunes

2003-01-01

The aim of this communication is to study with a new scope the conditions of the equilibrium in an air transport market where two competitive airlines are operating. Each airline is supposed to adopt a strategy maximizing its profit while its estimation of the demand has a fuzzy nature. This leads each company to optimize a program of its proposed services (frequency of the flights and ticket prices) characterized by some fuzzy parameters. The case of monopoly is being taken as a benchmark. Classical convex optimization can be used to solve this decision problem. This approach provides the airline with a new decision tool where uncertainty can be taken into account explicitly. The confrontation of the strategies of the companies, in the ease of duopoly, leads to the definition of a fuzzy equilibrium. This concept of fuzzy equilibrium is more general and can be applied to several other domains. The formulation of the optimization problem and the methodological consideration adopted for its resolution are presented in their general theoretical aspect. In the case of air transportation, where the conditions of management of operations are critical, this approach should offer to the manager elements needed to the consolidation of its decisions depending on the circumstances (ordinary, exceptional events,..) and to be prepared to face all possibilities. Keywords: air transportation, competition equilibrium, convex optimization , fuzzy modeling,

Cyclical parthenogenesis algorithm for layout optimization of truss structures with frequency constraints

NASA Astrophysics Data System (ADS)

Kaveh, A.; Zolghadr, A.

2017-08-01

Structural optimization with frequency constraints is seen as a challenging problem because it is associated with highly nonlinear, discontinuous and non-convex search spaces consisting of several local optima. Therefore, competent optimization algorithms are essential for addressing these problems. In this article, a newly developed metaheuristic method called the cyclical parthenogenesis algorithm (CPA) is used for layout optimization of truss structures subjected to frequency constraints. CPA is a nature-inspired, population-based metaheuristic algorithm, which imitates the reproductive and social behaviour of some animal species such as aphids, which alternate between sexual and asexual reproduction. The efficiency of the CPA is validated using four numerical examples.

Optimal Full Information Synthesis for Flexible Structures Implemented on Cray Supercomputers

NASA Technical Reports Server (NTRS)

Lind, Rick; Balas, Gary J.

1995-01-01

This paper considers an algorithm for synthesis of optimal controllers for full information feedback. The synthesis procedure reduces to a single linear matrix inequality which may be solved via established convex optimization algorithms. The computational cost of the optimization is investigated. It is demonstrated the problem dimension and corresponding matrices can become large for practical engineering problems. This algorithm represents a process that is impractical for standard workstations for large order systems. A flexible structure is presented as a design example. Control synthesis requires several days on a workstation but may be solved in a reasonable amount of time using a Cray supercomputer.

A new convexity measure for polygons.

PubMed

Zunic, Jovisa; Rosin, Paul L

2004-07-01

Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.

TH-EF-BRB-04: 4π Dynamic Conformal Arc Therapy Dynamic Conformal Arc Therapy (DCAT) for SBRT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiu, T; Long, T; Tian, Z.

2016-06-15

Purpose: To develop an efficient and effective trajectory optimization methodology for 4π dynamic conformal arc treatment (4π DCAT) with synchronized gantry and couch motion; and to investigate potential clinical benefits for stereotactic body radiation therapy (SBRT) to breast, lung, liver and spine tumors. Methods: The entire optimization framework for 4π DCAT inverse planning consists of two parts: 1) integer programming algorithm and 2) particle swarm optimization (PSO) algorithm. The integer programming is designed to find an optimal solution for arc delivery trajectory with both couch and gantry rotation, while PSO minimize a non-convex objective function based on the selected trajectorymore » and dose-volume constraints. In this study, control point interaction is explicitly taken into account. Beam trajectory was modeled as a series of control points connected together to form a deliverable path. With linear treatment planning objectives, a mixed-integer program (MIP) was formulated. Under mild assumptions, the MIP is tractable. Assigning monitor units to control points along the path can be integrated into the model and done by PSO. The developed 4π DCAT inverse planning strategy is evaluated on SBRT cases and compared to clinically treated plans. Results: The resultant dose distribution of this technique was evaluated between 3D conformal treatment plan generated by Pinnacle treatment planning system and 4π DCAT on a lung SBRT patient case. Both plans share the same scale of MU, 3038 and 2822 correspondingly to 3D conformal plan and 4π DCAT. The mean doses for most of OARs were greatly reduced at 32% (cord), 70% (esophagus), 2.8% (lung) and 42.4% (stomach). Conclusion: Initial results in this study show the proposed 4π DCAT treatment technique can achieve better OAR sparing and lower MUs, which indicates that the developed technique is promising for high dose SBRT to reduce the risk of secondary cancer.« less

Constrained Optimal Transport

NASA Astrophysics Data System (ADS)

Ekren, Ibrahim; Soner, H. Mete

2018-03-01

The classical duality theory of Kantorovich (C R (Doklady) Acad Sci URSS (NS) 37:199-201, 1942) and Kellerer (Z Wahrsch Verw Gebiete 67(4):399-432, 1984) for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice X with an order unit. The problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of X and the dual problem is defined on the bi-dual of X. These results are then applied to several extensions of the classical optimal transport.

Prostate segmentation: an efficient convex optimization approach with axial symmetry using 3-D TRUS and MR images.

PubMed

Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron

2014-04-01

We propose a novel global optimization-based approach to segmentation of 3-D prostate transrectal ultrasound (TRUS) and T2 weighted magnetic resonance (MR) images, enforcing inherent axial symmetry of prostate shapes to simultaneously adjust a series of 2-D slice-wise segmentations in a "global" 3-D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coherent continuous max-flow model (CCMFM), which derives a new and efficient duality-based algorithm, leading to a GPU-based implementation to achieve high computational speeds. Experiments with 25 3-D TRUS images and 30 3-D T2w MR images from our dataset, and 50 3-D T2w MR images from a public dataset, demonstrate that the proposed approach can segment a 3-D prostate TRUS/MR image within 5-6 s including 4-5 s for initialization, yielding a mean Dice similarity coefficient of 93.2%±2.0% for 3-D TRUS images and 88.5%±3.5% for 3-D MR images. The proposed method also yields relatively low intra- and inter-observer variability introduced by user manual initialization, suggesting a high reproducibility, independent of observers.

3D prostate TRUS segmentation using globally optimized volume-preserving prior.

PubMed

Qiu, Wu; Rajchl, Martin; Guo, Fumin; Sun, Yue; Ukwatta, Eranga; Fenster, Aaron; Yuan, Jing

2014-01-01

An efficient and accurate segmentation of 3D transrectal ultrasound (TRUS) images plays an important role in the planning and treatment of the practical 3D TRUS guided prostate biopsy. However, a meaningful segmentation of 3D TRUS images tends to suffer from US speckles, shadowing and missing edges etc, which make it a challenging task to delineate the correct prostate boundaries. In this paper, we propose a novel convex optimization based approach to extracting the prostate surface from the given 3D TRUS image, while preserving a new global volume-size prior. We, especially, study the proposed combinatorial optimization problem by convex relaxation and introduce its dual continuous max-flow formulation with the new bounded flow conservation constraint, which results in an efficient numerical solver implemented on GPUs. Experimental results using 12 patient 3D TRUS images show that the proposed approach while preserving the volume-size prior yielded a mean DSC of 89.5% +/- 2.4%, a MAD of 1.4 +/- 0.6 mm, a MAXD of 5.2 +/- 3.2 mm, and a VD of 7.5% +/- 6.2% in - 1 minute, deomonstrating the advantages of both accuracy and efficiency. In addition, the low standard deviation of the segmentation accuracy shows a good reliability of the proposed approach.

A Convex Formulation for Learning a Shared Predictive Structure from Multiple Tasks

PubMed Central

Chen, Jianhui; Tang, Lei; Liu, Jun; Ye, Jieping

2013-01-01

In this paper, we consider the problem of learning from multiple related tasks for improved generalization performance by extracting their shared structures. The alternating structure optimization (ASO) algorithm, which couples all tasks using a shared feature representation, has been successfully applied in various multitask learning problems. However, ASO is nonconvex and the alternating algorithm only finds a local solution. We first present an improved ASO formulation (iASO) for multitask learning based on a new regularizer. We then convert iASO, a nonconvex formulation, into a relaxed convex one (rASO). Interestingly, our theoretical analysis reveals that rASO finds a globally optimal solution to its nonconvex counterpart iASO under certain conditions. rASO can be equivalently reformulated as a semidefinite program (SDP), which is, however, not scalable to large datasets. We propose to employ the block coordinate descent (BCD) method and the accelerated projected gradient (APG) algorithm separately to find the globally optimal solution to rASO; we also develop efficient algorithms for solving the key subproblems involved in BCD and APG. The experiments on the Yahoo webpages datasets and the Drosophila gene expression pattern images datasets demonstrate the effectiveness and efficiency of the proposed algorithms and confirm our theoretical analysis. PMID:23520249

Sparse generalized linear model with L0 approximation for feature selection and prediction with big omics data.

PubMed

Liu, Zhenqiu; Sun, Fengzhu; McGovern, Dermot P

2017-01-01

Feature selection and prediction are the most important tasks for big data mining. The common strategies for feature selection in big data mining are L 1 , SCAD and MC+. However, none of the existing algorithms optimizes L 0 , which penalizes the number of nonzero features directly. In this paper, we develop a novel sparse generalized linear model (GLM) with L 0 approximation for feature selection and prediction with big omics data. The proposed approach approximate the L 0 optimization directly. Even though the original L 0 problem is non-convex, the problem is approximated by sequential convex optimizations with the proposed algorithm. The proposed method is easy to implement with only several lines of code. Novel adaptive ridge algorithms ( L 0 ADRIDGE) for L 0 penalized GLM with ultra high dimensional big data are developed. The proposed approach outperforms the other cutting edge regularization methods including SCAD and MC+ in simulations. When it is applied to integrated analysis of mRNA, microRNA, and methylation data from TCGA ovarian cancer, multilevel gene signatures associated with suboptimal debulking are identified simultaneously. The biological significance and potential clinical importance of those genes are further explored. The developed Software L 0 ADRIDGE in MATLAB is available at https://github.com/liuzqx/L0adridge.

3D prostate MR-TRUS non-rigid registration using dual optimization with volume-preserving constraint

NASA Astrophysics Data System (ADS)

Qiu, Wu; Yuan, Jing; Fenster, Aaron

2016-03-01

We introduce an efficient and novel convex optimization-based approach to the challenging non-rigid registration of 3D prostate magnetic resonance (MR) and transrectal ultrasound (TRUS) images, which incorporates a new volume preserving constraint to essentially improve the accuracy of targeting suspicious regions during the 3D TRUS guided prostate biopsy. Especially, we propose a fast sequential convex optimization scheme to efficiently minimize the employed highly nonlinear image fidelity function using the robust multi-channel modality independent neighborhood descriptor (MIND) across the two modalities of MR and TRUS. The registration accuracy was evaluated using 10 patient images by calculating the target registration error (TRE) using manually identified corresponding intrinsic fiducials in the whole prostate gland. We also compared the MR and TRUS manually segmented prostate surfaces in the registered images in terms of the Dice similarity coefficient (DSC), mean absolute surface distance (MAD), and maximum absolute surface distance (MAXD). Experimental results showed that the proposed method with the introduced volume-preserving prior significantly improves the registration accuracy comparing to the method without the volume-preserving constraint, by yielding an overall mean TRE of 2:0+/-0:7 mm, and an average DSC of 86:5+/-3:5%, MAD of 1:4+/-0:6 mm and MAXD of 6:5+/-3:5 mm.

Behavior of Machine Learning Algorithms in Adversarial Environments

DTIC Science & Technology

2010-11-23

handwriting recog- nition [cf., Plamondon and Srihari, 2000], they also have potentially far-reaching utility for many applications in security, networking...cost of the largest ℓp cost ball that fits entirely within their convex hull; let’s say this cost is C† ≤ C+0 . To achieve ǫ-multiplicative optimality...optimal on Fconvex,’+’ for ℓ2 costs. The proof of this result is in Appendix C.4. This result says that there is no algorithm can generally achieve ǫ

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

Image processing and reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chartrand, Rick

2012-06-15

This talk will examine some mathematical methods for image processing and the solution of underdetermined, linear inverse problems. The talk will have a tutorial flavor, mostly accessible to undergraduates, while still presenting research results. The primary approach is the use of optimization problems. We will find that relaxing the usual assumption of convexity will give us much better results.

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

PubMed Central

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

A convex optimization method for self-organization in dynamic (FSO/RF) wireless networks

NASA Astrophysics Data System (ADS)

Llorca, Jaime; Davis, Christopher C.; Milner, Stuart D.

2008-08-01

Next generation communication networks are becoming increasingly complex systems. Previously, we presented a novel physics-based approach to model dynamic wireless networks as physical systems which react to local forces exerted on network nodes. We showed that under clear atmospheric conditions the network communication energy can be modeled as the potential energy of an analogous spring system and presented a distributed mobility control algorithm where nodes react to local forces driving the network to energy minimizing configurations. This paper extends our previous work by including the effects of atmospheric attenuation and transmitted power constraints in the optimization problem. We show how our new formulation still results in a convex energy minimization problem. Accordingly, an updated force-driven mobility control algorithm is presented. Forces on mobile backbone nodes are computed as the negative gradient of the new energy function. Results show how in the presence of atmospheric obscuration stronger forces are exerted on network nodes that make them move closer to each other, avoiding loss of connectivity. We show results in terms of network coverage and backbone connectivity and compare the developed algorithms for different scenarios.

Equivalent Relaxations of Optimal Power Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bose, S; Low, SH; Teeraratkul, T

2015-03-01

Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results implymore » that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second-order cone relaxation. Therefore, for mesh networks, one should either solve the chordal relaxation or the SOCP relaxation, trading off tightness and the required computational effort. Simulations are used to illustrate these results.« less

AUC-based biomarker ensemble with an application on gene scores predicting low bone mineral density.

PubMed

Zhao, X G; Dai, W; Li, Y; Tian, L

2011-11-01

The area under the receiver operating characteristic (ROC) curve (AUC), long regarded as a 'golden' measure for the predictiveness of a continuous score, has propelled the need to develop AUC-based predictors. However, the AUC-based ensemble methods are rather scant, largely due to the fact that the associated objective function is neither continuous nor concave. Indeed, there is no reliable numerical algorithm identifying optimal combination of a set of biomarkers to maximize the AUC, especially when the number of biomarkers is large. We have proposed a novel AUC-based statistical ensemble methods for combining multiple biomarkers to differentiate a binary response of interest. Specifically, we propose to replace the non-continuous and non-convex AUC objective function by a convex surrogate loss function, whose minimizer can be efficiently identified. With the established framework, the lasso and other regularization techniques enable feature selections. Extensive simulations have demonstrated the superiority of the new methods to the existing methods. The proposal has been applied to a gene expression dataset to construct gene expression scores to differentiate elderly women with low bone mineral density (BMD) and those with normal BMD. The AUCs of the resulting scores in the independent test dataset has been satisfactory. Aiming for directly maximizing AUC, the proposed AUC-based ensemble method provides an efficient means of generating a stable combination of multiple biomarkers, which is especially useful under the high-dimensional settings. lutian@stanford.edu. Supplementary data are available at Bioinformatics online.

Variational-based segmentation of bio-pores in tomographic images

NASA Astrophysics Data System (ADS)

Bauer, Benjamin; Cai, Xiaohao; Peth, Stephan; Schladitz, Katja; Steidl, Gabriele

2017-01-01

X-ray computed tomography (CT) combined with a quantitative analysis of the resulting volume images is a fruitful technique in soil science. However, the variations in X-ray attenuation due to different soil components keep the segmentation of single components within these highly heterogeneous samples a challenging problem. Particularly demanding are bio-pores due to their elongated shape and the low gray value difference to the surrounding soil structure. Recently, variational models in connection with algorithms from convex optimization were successfully applied for image segmentation. In this paper we apply these methods for the first time for the segmentation of bio-pores in CT images of soil samples. We introduce a novel convex model which enforces smooth boundaries of bio-pores and takes the varying attenuation values in the depth into account. Segmentation results are reported for different real-world 3D data sets as well as for simulated data. These results are compared with two gray value thresholding methods, namely indicator kriging and a global thresholding procedure, and with a morphological approach. Pros and cons of the methods are assessed by considering geometric features of the segmented bio-pore systems. The variational approach features well-connected smooth pores while not detecting smaller or shallower pores. This is an advantage in cases where the main bio-pores network is of interest and where infillings, e.g., excrements of earthworms, would result in losing pore connections as observed for the other thresholding methods.

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, wemore » present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.« less

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

DOE PAGES

Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.; ...

2017-05-08

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, wemore » present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.« less

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

A Multi-Hop Energy Neutral Clustering Algorithm for Maximizing Network Information Gathering in Energy Harvesting Wireless Sensor Networks.

PubMed

Yang, Liu; Lu, Yinzhi; Zhong, Yuanchang; Wu, Xuegang; Yang, Simon X

2015-12-26

Energy resource limitation is a severe problem in traditional wireless sensor networks (WSNs) because it restricts the lifetime of network. Recently, the emergence of energy harvesting techniques has brought with them the expectation to overcome this problem. In particular, it is possible for a sensor node with energy harvesting abilities to work perpetually in an Energy Neutral state. In this paper, a Multi-hop Energy Neutral Clustering (MENC) algorithm is proposed to construct the optimal multi-hop clustering architecture in energy harvesting WSNs, with the goal of achieving perpetual network operation. All cluster heads (CHs) in the network act as routers to transmit data to base station (BS) cooperatively by a multi-hop communication method. In addition, by analyzing the energy consumption of intra- and inter-cluster data transmission, we give the energy neutrality constraints. Under these constraints, every sensor node can work in an energy neutral state, which in turn provides perpetual network operation. Furthermore, the minimum network data transmission cycle is mathematically derived using convex optimization techniques while the network information gathering is maximal. Simulation results show that our protocol can achieve perpetual network operation, so that the consistent data delivery is guaranteed. In addition, substantial improvements on the performance of network throughput are also achieved as compared to the famous traditional clustering protocol LEACH and recent energy harvesting aware clustering protocols.

A Multi-Hop Energy Neutral Clustering Algorithm for Maximizing Network Information Gathering in Energy Harvesting Wireless Sensor Networks

PubMed Central

Yang, Liu; Lu, Yinzhi; Zhong, Yuanchang; Wu, Xuegang; Yang, Simon X.

2015-01-01

Energy resource limitation is a severe problem in traditional wireless sensor networks (WSNs) because it restricts the lifetime of network. Recently, the emergence of energy harvesting techniques has brought with them the expectation to overcome this problem. In particular, it is possible for a sensor node with energy harvesting abilities to work perpetually in an Energy Neutral state. In this paper, a Multi-hop Energy Neutral Clustering (MENC) algorithm is proposed to construct the optimal multi-hop clustering architecture in energy harvesting WSNs, with the goal of achieving perpetual network operation. All cluster heads (CHs) in the network act as routers to transmit data to base station (BS) cooperatively by a multi-hop communication method. In addition, by analyzing the energy consumption of intra- and inter-cluster data transmission, we give the energy neutrality constraints. Under these constraints, every sensor node can work in an energy neutral state, which in turn provides perpetual network operation. Furthermore, the minimum network data transmission cycle is mathematically derived using convex optimization techniques while the network information gathering is maximal. Simulation results show that our protocol can achieve perpetual network operation, so that the consistent data delivery is guaranteed. In addition, substantial improvements on the performance of network throughput are also achieved as compared to the famous traditional clustering protocol LEACH and recent energy harvesting aware clustering protocols. PMID:26712764

A new neural network model for solving random interval linear programming problems.

PubMed

Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza

2017-05-01

This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.

Takagi-Sugeno fuzzy model based robust dissipative control for uncertain flexible spacecraft with saturated time-delay input.

PubMed

Xu, Shidong; Sun, Guanghui; Sun, Weichao

2017-01-01

In this paper, the problem of robust dissipative control is investigated for uncertain flexible spacecraft based on Takagi-Sugeno (T-S) fuzzy model with saturated time-delay input. Different from most existing strategies, T-S fuzzy approximation approach is used to model the nonlinear dynamics of flexible spacecraft. Simultaneously, the physical constraints of system, like input delay, input saturation, and parameter uncertainties, are also taken care of in the fuzzy model. By employing Lyapunov-Krasovskii method and convex optimization technique, a novel robust controller is proposed to implement rest-to-rest attitude maneuver for flexible spacecraft, and the guaranteed dissipative performance enables the uncertain closed-loop system to reject the influence of elastic vibrations and external disturbances. Finally, an illustrative design example integrated with simulation results are provided to confirm the applicability and merits of the developed control strategy. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Misaligned Image Integration With Local Linear Model.

PubMed

Baba, Tatsuya; Matsuoka, Ryo; Shirai, Keiichiro; Okuda, Masahiro

2016-05-01

We present a new image integration technique for a flash and long-exposure image pair to capture a dark scene without incurring blurring or noisy artifacts. Most existing methods require well-aligned images for the integration, which is often a burdensome restriction in practical use. We address this issue by locally transferring the colors of the flash images using a small fraction of the corresponding pixels in the long-exposure images. We formulate the image integration as a convex optimization problem with the local linear model. The proposed method makes it possible to integrate the color of the long-exposure image with the detail of the flash image without causing any harmful effects to its contrast, where we do not need perfect alignment between the images by virtue of our new integration principle. We show that our method successfully outperforms the state of the art in the image integration and reference-based color transfer for challenging misaligned data sets.

Reduced rank regression via adaptive nuclear norm penalization

PubMed Central

Chen, Kun; Dong, Hongbo; Chan, Kung-Sik

2014-01-01

Summary We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex penalized regression method has a global optimal solution obtained from an adaptively soft-thresholded singular value decomposition. The method is computationally efficient, and the resulting solution path is continuous. The rank consistency of and prediction/estimation performance bounds for the estimator are established for a high-dimensional asymptotic regime. Simulation studies and an application in genetics demonstrate its efficacy. PMID:25045172

Distributed Optimization of Multi-Agent Systems: Framework, Local Optimizer, and Applications

NASA Astrophysics Data System (ADS)

Zu, Yue

Convex optimization problem can be solved in a centralized or distributed manner. Compared with centralized methods based on single-agent system, distributed algorithms rely on multi-agent systems with information exchanging among connected neighbors, which leads to great improvement on the system fault tolerance. Thus, a task within multi-agent system can be completed with presence of partial agent failures. By problem decomposition, a large-scale problem can be divided into a set of small-scale sub-problems that can be solved in sequence/parallel. Hence, the computational complexity is greatly reduced by distributed algorithm in multi-agent system. Moreover, distributed algorithm allows data collected and stored in a distributed fashion, which successfully overcomes the drawbacks of using multicast due to the bandwidth limitation. Distributed algorithm has been applied in solving a variety of real-world problems. Our research focuses on the framework and local optimizer design in practical engineering applications. In the first one, we propose a multi-sensor and multi-agent scheme for spatial motion estimation of a rigid body. Estimation performance is improved in terms of accuracy and convergence speed. Second, we develop a cyber-physical system and implement distributed computation devices to optimize the in-building evacuation path when hazard occurs. The proposed Bellman-Ford Dual-Subgradient path planning method relieves the congestion in corridor and the exit areas. At last, highway traffic flow is managed by adjusting speed limits to minimize the fuel consumption and travel time in the third project. Optimal control strategy is designed through both centralized and distributed algorithm based on convex problem formulation. Moreover, a hybrid control scheme is presented for highway network travel time minimization. Compared with no controlled case or conventional highway traffic control strategy, the proposed hybrid control strategy greatly reduces total travel time on test highway network.

Control of water distribution networks with dynamic DMA topology using strictly feasible sequential convex programming

NASA Astrophysics Data System (ADS)

Wright, Robert; Abraham, Edo; Parpas, Panos; Stoianov, Ivan

2015-12-01

The operation of water distribution networks (WDN) with a dynamic topology is a recently pioneered approach for the advanced management of District Metered Areas (DMAs) that integrates novel developments in hydraulic modeling, monitoring, optimization, and control. A common practice for leakage management is the sectorization of WDNs into small zones, called DMAs, by permanently closing isolation valves. This facilitates water companies to identify bursts and estimate leakage levels by measuring the inlet flow for each DMA. However, by permanently closing valves, a number of problems have been created including reduced resilience to failure and suboptimal pressure management. By introducing a dynamic topology to these zones, these disadvantages can be eliminated while still retaining the DMA structure for leakage monitoring. In this paper, a novel optimization method based on sequential convex programming (SCP) is outlined for the control of a dynamic topology with the objective of reducing average zone pressure (AZP). A key attribute for control optimization is reliable convergence. To achieve this, the SCP method we propose guarantees that each optimization step is strictly feasible, resulting in improved convergence properties. By using a null space algorithm for hydraulic analyses, the computations required are also significantly reduced. The optimized control is actuated on a real WDN operated with a dynamic topology. This unique experimental program incorporates a number of technologies set up with the objective of investigating pioneering developments in WDN management. Preliminary results indicate AZP reductions for a dynamic topology of up to 6.5% over optimally controlled fixed topology DMAs. This article was corrected on 12 JAN 2016. See the end of the full text for details.

Primal-dual techniques for online algorithms and mechanisms

NASA Astrophysics Data System (ADS)

Liaghat, Vahid

An offline algorithm is one that knows the entire input in advance. An online algorithm, however, processes its input in a serial fashion. In contrast to offline algorithms, an online algorithm works in a local fashion and has to make irrevocable decisions without having the entire input. Online algorithms are often not optimal since their irrevocable decisions may turn out to be inefficient after receiving the rest of the input. For a given online problem, the goal is to design algorithms which are competitive against the offline optimal solutions. In a classical offline scenario, it is often common to see a dual analysis of problems that can be formulated as a linear or convex program. Primal-dual and dual-fitting techniques have been successfully applied to many such problems. Unfortunately, the usual tricks come short in an online setting since an online algorithm should make decisions without knowing even the whole program. In this thesis, we study the competitive analysis of fundamental problems in the literature such as different variants of online matching and online Steiner connectivity, via online dual techniques. Although there are many generic tools for solving an optimization problem in the offline paradigm, in comparison, much less is known for tackling online problems. The main focus of this work is to design generic techniques for solving integral linear optimization problems where the solution space is restricted via a set of linear constraints. A general family of these problems are online packing/covering problems. Our work shows that for several seemingly unrelated problems, primal-dual techniques can be successfully applied as a unifying approach for analyzing these problems. We believe this leads to generic algorithmic frameworks for solving online problems. In the first part of the thesis, we show the effectiveness of our techniques in the stochastic settings and their applications in Bayesian mechanism design. In particular, we introduce new techniques for solving a fundamental linear optimization problem, namely, the stochastic generalized assignment problem (GAP). This packing problem generalizes various problems such as online matching, ad allocation, bin packing, etc. We furthermore show applications of such results in the mechanism design by introducing Prophet Secretary, a novel Bayesian model for online auctions. In the second part of the thesis, we focus on the covering problems. We develop the framework of "Disk Painting" for a general class of network design problems that can be characterized by proper functions. This class generalizes the node-weighted and edge-weighted variants of several well-known Steiner connectivity problems. We furthermore design a generic technique for solving the prize-collecting variants of these problems when there exists a dual analysis for the non-prize-collecting counterparts. Hence, we solve the online prize-collecting variants of several network design problems for the first time. Finally we focus on designing techniques for online problems with mixed packing/covering constraints. We initiate the study of degree-bounded graph optimization problems in the online setting by designing an online algorithm with a tight competitive ratio for the degree-bounded Steiner forest problem. We hope these techniques establishes a starting point for the analysis of the important class of online degree-bounded optimization on graphs.

Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for continuous optimization problems. In this Part II of the paper, we study discrete problems, such as those involving user scheduling, which are considerably more difficult to solve. Unlike the continuous problems, discrete or mixed discrete-continuous problems normally cannot be recast as convex problems. In contrast to the common heuristic of relaxing the discrete variables, this work reformulates the original problem in an FP form amenable to distributed combinatorial optimization. The paper illustrates this methodology by tackling the important and challenging problem of uplink coordinated multi-cell user scheduling in wireless cellular systems. Uplink scheduling is more challenging than downlink scheduling, because uplink user scheduling decisions significantly affect the interference pattern in nearby cells. Further, the discrete scheduling variable needs to be optimized jointly with continuous variables such as transmit power levels and beamformers. The main idea of the proposed FP approach is to decouple the interaction among the interfering links, thereby permitting a distributed and joint optimization of the discrete and continuous variables with provable convergence. The paper shows that the well-known weighted minimum mean-square-error (WMMSE) algorithm can also be derived from a particular use of FP; but our proposed FP-based method significantly outperforms WMMSE when discrete user scheduling variables are involved, both in term of run-time efficiency and optimizing results.

Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model

NASA Astrophysics Data System (ADS)

Ushijima, Timothy T.; Yeh, William W.-G.

2013-10-01

An optimal experimental design algorithm is developed to select locations for a network of observation wells that provide maximum information about unknown groundwater pumping in a confined, anisotropic aquifer. The design uses a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. The formulated optimization problem is non-convex and contains integer variables necessitating a combinatorial search. Given a realistic large-scale model, the size of the combinatorial search required can make the problem difficult, if not impossible, to solve using traditional mathematical programming techniques. Genetic algorithms (GAs) can be used to perform the global search; however, because a GA requires a large number of calls to a groundwater model, the formulated optimization problem still may be infeasible to solve. As a result, proper orthogonal decomposition (POD) is applied to the groundwater model to reduce its dimensionality. Then, the information matrix in the full model space can be searched without solving the full model. Results from a small-scale test case show identical optimal solutions among the GA, integer programming, and exhaustive search methods. This demonstrates the GA's ability to determine the optimal solution. In addition, the results show that a GA with POD model reduction is several orders of magnitude faster in finding the optimal solution than a GA using the full model. The proposed experimental design algorithm is applied to a realistic, two-dimensional, large-scale groundwater problem. The GA converged to a solution for this large-scale problem.

A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints.

PubMed

Liang, X B; Wang, J

2000-01-01

This paper presents a continuous-time recurrent neural-network model for nonlinear optimization with any continuously differentiable objective function and bound constraints. Quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network. The proposed recurrent neural network has the following characteristics. 1) It is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network. If the objective function to be minimized is convex, then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network. 2) The recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region. 3) The recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region. 4) For minimizing any strictly convex quadratic objective function subject to bound constraints, the recurrent neural network is globally exponentially stable for almost any positive network parameters. Simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints.

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, James C.; Scharf, Daniel P.

2011-01-01

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Inverse problems in complex material design: Applications to non-crystalline solids

NASA Astrophysics Data System (ADS)

Biswas, Parthapratim; Drabold, David; Elliott, Stephen

The design of complex amorphous materials is one of the fundamental problems in disordered condensed-matter science. While impressive developments of ab-initio simulation methods during the past several decades have brought tremendous success in understanding materials property from micro- to mesoscopic length scales, a major drawback is that they fail to incorporate existing knowledge of the materials in simulation methodologies. Since an essential feature of materials design is the synergy between experiment and theory, a properly developed approach to design materials should be able to exploit all available knowledge of the materials from measured experimental data. In this talk, we will address the design of complex disordered materials as an inverse problem involving experimental data and available empirical information. We show that the problem can be posed as a multi-objective non-convex optimization program, which can be addressed using a number of recently-developed bio-inspired global optimization techniques. In particular, we will discuss how a population-based stochastic search procedure can be used to determine the structure of non-crystalline solids (e.g. a-SiH, a-SiO2, amorphous graphene, and Fe and Ni clusters). The work is partially supported by NSF under Grant Nos. DMR 1507166 and 1507670.

Efficient methods for overlapping group lasso.

PubMed

Yuan, Lei; Liu, Jun; Ye, Jieping

2013-09-01

The group Lasso is an extension of the Lasso for feature selection on (predefined) nonoverlapping groups of features. The nonoverlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. Our methods and theoretical results are then generalized to tackle the general overlapping group Lasso formulation based on the l(q) norm. We further extend our algorithm to solve a nonconvex overlapping group Lasso formulation based on the capped norm regularization, which reduces the estimation bias introduced by the convex penalty. We have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms. Results also demonstrate the effectiveness of the nonconvex formulation for overlapping group Lasso.

Walking, running, and resting under time, distance, and average speed constraints: optimality of walk-run-rest mixtures.

PubMed

Long, Leroy L; Srinivasan, Manoj

2013-04-06

On a treadmill, humans switch from walking to running beyond a characteristic transition speed. Here, we study human choice between walking and running in a more ecological (non-treadmill) setting. We asked subjects to travel a given distance overground in a given allowed time duration. During this task, the subjects carried, and could look at, a stopwatch that counted down to zero. As expected, if the total time available were large, humans walk the whole distance. If the time available were small, humans mostly run. For an intermediate total time, humans often use a mixture of walking at a slow speed and running at a higher speed. With analytical and computational optimization, we show that using a walk-run mixture at intermediate speeds and a walk-rest mixture at the lowest average speeds is predicted by metabolic energy minimization, even with costs for transients-a consequence of non-convex energy curves. Thus, sometimes, steady locomotion may not be energy optimal, and not preferred, even in the absence of fatigue. Assuming similar non-convex energy curves, we conjecture that similar walk-run mixtures may be energetically beneficial to children following a parent and animals on long leashes. Humans and other animals might also benefit energetically from alternating between moving forward and standing still on a slow and sufficiently long treadmill.

Walking, running, and resting under time, distance, and average speed constraints: optimality of walk–run–rest mixtures

PubMed Central

Long, Leroy L.; Srinivasan, Manoj

2013-01-01

On a treadmill, humans switch from walking to running beyond a characteristic transition speed. Here, we study human choice between walking and running in a more ecological (non-treadmill) setting. We asked subjects to travel a given distance overground in a given allowed time duration. During this task, the subjects carried, and could look at, a stopwatch that counted down to zero. As expected, if the total time available were large, humans walk the whole distance. If the time available were small, humans mostly run. For an intermediate total time, humans often use a mixture of walking at a slow speed and running at a higher speed. With analytical and computational optimization, we show that using a walk–run mixture at intermediate speeds and a walk–rest mixture at the lowest average speeds is predicted by metabolic energy minimization, even with costs for transients—a consequence of non-convex energy curves. Thus, sometimes, steady locomotion may not be energy optimal, and not preferred, even in the absence of fatigue. Assuming similar non-convex energy curves, we conjecture that similar walk–run mixtures may be energetically beneficial to children following a parent and animals on long leashes. Humans and other animals might also benefit energetically from alternating between moving forward and standing still on a slow and sufficiently long treadmill. PMID:23365192

Integration of mechanism and control for large-angle slew maneuvers of flexible structures

NASA Technical Reports Server (NTRS)

Chew, Meng-Sang

1991-01-01

A rolling contact noncircular gear system is applied to assist a desired controller in the slewing of a flexible space structure. The varying gear ratio in cooperation with the controller results in lower feedback gains at the controller, as well as considerably reducing flexural vibrations of the space structure. The noncircular gears consist of a pair of convex noncircular cylinders with specially designed profiles that are synthesized in conjunction with the optimal controller gains for minimizing the flexural vibrations of flexible structure during a slew maneuver. Convexity of the cylindrical profiles for this noncircular gear device must be ensured to maintain rolling contact between the two cylinders. Simulations of slewing control tasks for two kinds of flexible space structures, such as a planar flexible beam and the planar articulated flexible beams, are presented.

Solution for a bipartite Euclidean traveling-salesman problem in one dimension

NASA Astrophysics Data System (ADS)

Caracciolo, Sergio; Di Gioacchino, Andrea; Gherardi, Marco; Malatesta, Enrico M.

2018-05-01

The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing cost function when the points are thrown independently and with an identical probability distribution in a compact interval. We compute the average optimal cost for every number of points when the distance function is the square of the Euclidean distance. We also show that the average optimal cost is not a self-averaging quantity by explicitly computing the variance of its distribution in the thermodynamic limit. Moreover, we prove that the cost of the optimal cycle is not smaller than twice the cost of the optimal assignment of the same set of points. Interestingly, this bound is saturated in the thermodynamic limit.

Solution for a bipartite Euclidean traveling-salesman problem in one dimension.

PubMed

Caracciolo, Sergio; Di Gioacchino, Andrea; Gherardi, Marco; Malatesta, Enrico M

2018-05-01

The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing cost function when the points are thrown independently and with an identical probability distribution in a compact interval. We compute the average optimal cost for every number of points when the distance function is the square of the Euclidean distance. We also show that the average optimal cost is not a self-averaging quantity by explicitly computing the variance of its distribution in the thermodynamic limit. Moreover, we prove that the cost of the optimal cycle is not smaller than twice the cost of the optimal assignment of the same set of points. Interestingly, this bound is saturated in the thermodynamic limit.

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.

2000-01-01

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

Laser micromilling of convex microfluidic channels onto glassy carbon for glass molding dies

NASA Astrophysics Data System (ADS)

Tseng, Shih-Feng; Chen, Ming-Fei; Hsiao, Wen-Tse; Huang, Chien-Yao; Yang, Chung-Heng; Chen, Yu-Sheng

2014-06-01

This study reports the fabrication of convex microfluidic channels on glassy carbon using an ultraviolet laser processing system to produce glass molding dies. The laser processing parameters, including various laser fluences and scanning speeds of galvanometers, were adjusted to mill a convex microchannel on a glassy carbon substrate to identify the effects of material removal. The machined glassy carbon substrate was then applied as a glass molding die to fabricate a glass-based microfluidic biochip. The surface morphology, milled width and depth, and surface roughness of the microchannel die after laser micromilling were examined using a three-dimensional confocal laser scanning microscope. This study also investigates the transcription rate of microchannels after the glass molding process. To produce a 180 μm high microchannel on the GC substrate, the optimal number of milled cycles, laser fluence, and scanning speed were 25, 4.9 J/cm2, and 200 mm/s, respectively. The width, height, and surface roughness of milled convex microchannels were 119.6±0.217 μm, 180.26±0.01 μm, and 0.672±0.08 μm, respectively. These measured values were close to the predicted values and suitable for a glass molding die. After the glass molding process, a typical glass-based microchannel chip was formed at a molding temperature of 660 °C and the molding force of 0.45 kN. The transcription rates of the microchannel width and depth were 100% and 99.6%, respectively. Thus, the proposed approach is suitable for performing in chemical, biochemical, or medical reactions.

Designing Robust and Resilient Tactical MANETs

DTIC Science & Technology

2014-09-25

Bounds on the Throughput Efficiency of Greedy Maximal Scheduling in Wireless Networks , IEEE/ACM Transactions on Networking , (06 2011): 0. doi: N... Wireless Sensor Networks and Effects of Long Range Dependant Data, Special IWSM Issue of Sequential Analysis, (11 2012): 0. doi: A. D. Dominguez...Bushnell, R. Poovendran. A Convex Optimization Approach for Clone Detection in Wireless Sensor Networks , Pervasive and Mobile Computing, (01 2012

EEG Dynamics Reflect the Distinct Cognitive Process of Optic Problem Solving

PubMed Central

She, Hsiao-Ching; Jung, Tzyy-Ping; Chou, Wen-Chi; Huang, Li-Yu; Wang, Chia-Yu; Lin, Guan-Yu

2012-01-01

This study explores the changes in electroencephalographic (EEG) activity associated with the performance of solving an optics maze problem. College students (N = 37) were instructed to construct three solutions to the optical maze in a Web-based learning environment, which required some knowledge of physics. The subjects put forth their best effort to minimize the number of convexes and mirrors needed to guide the image of an object from the entrance to the exit of the maze. This study examines EEG changes in different frequency bands accompanying varying demands on the cognitive process of providing solutions. Results showed that the mean power of θ, α1, α2, and β1 significantly increased as the number of convexes and mirrors used by the students decreased from solution 1 to 3. Moreover, the mean power of θ and α1 significantly increased when the participants constructed their personal optimal solution (the least total number of mirrors and lens used by students) compared to their non-personal optimal solution. In conclusion, the spectral power of frontal, frontal midline and posterior theta, posterior alpha, and temporal beta increased predominantly as the task demands and task performance increased. PMID:22815800

Shape and Spatially-Varying Reflectance Estimation from Virtual Exemplars.

PubMed

Hui, Zhuo; Sankaranarayanan, Aswin C

2017-10-01

This paper addresses the problem of estimating the shape of objects that exhibit spatially-varying reflectance. We assume that multiple images of the object are obtained under a fixed view-point and varying illumination, i.e., the setting of photometric stereo. At the core of our techniques is the assumption that the BRDF at each pixel lies in the non-negative span of a known BRDF dictionary. This assumption enables a per-pixel surface normal and BRDF estimation framework that is computationally tractable and requires no initialization in spite of the underlying problem being non-convex. Our estimation framework first solves for the surface normal at each pixel using a variant of example-based photometric stereo. We design an efficient multi-scale search strategy for estimating the surface normal and subsequently, refine this estimate using a gradient descent procedure. Given the surface normal estimate, we solve for the spatially-varying BRDF by constraining the BRDF at each pixel to be in the span of the BRDF dictionary; here, we use additional priors to further regularize the solution. A hallmark of our approach is that it does not require iterative optimization techniques nor the need for careful initialization, both of which are endemic to most state-of-the-art techniques. We showcase the performance of our technique on a wide range of simulated and real scenes where we outperform competing methods.

Graph Design via Convex Optimization: Online and Distributed Perspectives

NASA Astrophysics Data System (ADS)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation problems in sensor networks, multi-agent coordination. Distributed optimization aims to optimize a global objective function formed by summation of coupled local functions over a graph via only local communication and computation. We developed a weighted proximal ADMM for distributed optimization using graph structure. This fully distributed, single-loop algorithm allows simultaneous updates and can be viewed as a generalization of existing algorithms. More importantly, we achieve faster convergence by jointly designing graph weights and algorithm parameters. Finally, we propose a new problem on networks called Online Network Formation Problem: starting with a base graph and a set of candidate edges, at each round of the game, player one first chooses a candidate edge and reveals it to player two, then player two decides whether to accept it; player two can only accept limited number of edges and make online decisions with the goal to achieve the best properties of the synthesized network. The network properties considered include the number of spanning trees, algebraic connectivity and total effective resistance. These network formation games arise in a variety of cooperative multiagent systems. We propose a primal-dual algorithm framework for the general online network formation game, and analyze the algorithm performance by the competitive ratio and regret.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning

NASA Astrophysics Data System (ADS)

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-08-01

{{\\ell }2,1} -minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the {{\\ell }2,1} -based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the {{\\ell }2,1} -minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the {{\\ell }2,1} -minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the {{\\ell }2,1} -minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning.

PubMed

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-07-20

[Formula: see text]-minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the [Formula: see text]-based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the [Formula: see text]-minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the [Formula: see text]-minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the [Formula: see text]-minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

Rapid optimization of tension distribution for cable-driven parallel manipulators with redundant cables

NASA Astrophysics Data System (ADS)

Ouyang, Bo; Shang, Weiwei

2016-03-01

The solution of tension distributions is infinite for cable-driven parallel manipulators(CDPMs) with redundant cables. A rapid optimization method for determining the optimal tension distribution is presented. The new optimization method is primarily based on the geometry properties of a polyhedron and convex analysis. The computational efficiency of the optimization method is improved by the designed projection algorithm, and a fast algorithm is proposed to determine which two of the lines are intersected at the optimal point. Moreover, a method for avoiding the operating point on the lower tension limit is developed. Simulation experiments are implemented on a six degree-of-freedom(6-DOF) CDPM with eight cables, and the results indicate that the new method is one order of magnitude faster than the standard simplex method. The optimal distribution of tension distribution is thus rapidly established on real-time by the proposed method.

Multi Objective Controller Design for Linear System via Optimal Interpolation

NASA Technical Reports Server (NTRS)

Ozbay, Hitay

1996-01-01

We propose a methodology for the design of a controller which satisfies a set of closed-loop objectives simultaneously. The set of objectives consists of: (1) pole placement, (2) decoupled command tracking of step inputs at steady-state, and (3) minimization of step response transients with respect to envelope specifications. We first obtain a characterization of all controllers placing the closed-loop poles in a prescribed region of the complex plane. In this characterization, the free parameter matrix Q(s) is to be determined to attain objectives (2) and (3). Objective (2) is expressed as determining a Pareto optimal solution to a vector valued optimization problem. The solution of this problem is obtained by transforming it to a scalar convex optimization problem. This solution determines Q(O) and the remaining freedom in choosing Q(s) is used to satisfy objective (3). We write Q(s) = (l/v(s))bar-Q(s) for a prescribed polynomial v(s). Bar-Q(s) is a polynomial matrix which is arbitrary except that Q(O) and the order of bar-Q(s) are fixed. Obeying these constraints bar-Q(s) is now to be 'shaped' to minimize the step response characteristics of specific input/output pairs according to the maximum envelope violations. This problem is expressed as a vector valued optimization problem using the concept of Pareto optimality. We then investigate a scalar optimization problem associated with this vector valued problem and show that it is convex. The organization of the report is as follows. The next section includes some definitions and preliminary lemmas. We then give the problem statement which is followed by a section including a detailed development of the design procedure. We then consider an aircraft control example. The last section gives some concluding remarks. The Appendix includes the proofs of technical lemmas, printouts of computer programs, and figures.

The LSST Optical System

NASA Astrophysics Data System (ADS)

Liang, M.; Seppala, L.; Sweeney, D.; LSST Project Team

2005-12-01

The 8.4m Large Synoptic Survey Telescope facility will digitally survey the entire visible sky. It will explore the nature of dark matter and dark energy, open the faint optical transient time window and catalog earth-crossing asteroids > 300m diameter. We present the design of an f/1.25 modified Paul-Baker or Laux telescope with etendue (A--Ω product) of >318m2 deg2 , >50× beyond any existing facility. The optical design, over a 3.5-degree diameter field of view (9.62 deg2), delivers superb ˜ 0.2 arcsec FWHM images over 6 spectral bands covering 325--1000 nm. The flat focal surface has a plate scale of 51 microns/arcsec, matching the 10 microns pixels of a large 0.65 m diameter mosaic digital detector. The f/1.17 primary can be made using polishing techniques and metrology methods pioneered at the University of Arizona Mirror Lab for the 8.4 m f/1.1 Large Binocular Telescope primaries. The 3.4 m convex secondary is twice the size of the largest convex secondary yet manufactured; the 1.7 m MMT f/5 secondary. We show a fabrication and testing plan for this optic, which has less than 40 microns asphericity from best fit sphere. Five separate null test or alignment tests are built in as part of the optimization of the entire telescope: the three lenses separately, the combination of the first two lenses and the three mirror telescope system, without the camera corrector optics. All five tests help to ensure practicable telescope design.

Deflectometric analysis of high volume injection molds for production of occupational eye wear.

PubMed

Speck, Alexis; Zelzer, Benedikt; Speich, Marco; Börret, Rainer; Langenbucher, Achim; Eppig, Timo

2013-12-01

Most of the protective eye wear devices currently on the market are manufactured on simple polycarbonate shields, produced by injection molding techniques. Despite high importance of optical quality, injection molds are rarely inspected for surface quality before or during the manufacturing process. Quality degradation is mainly monitored by optical testing of the molded parts. The purpose of this work was to validate a non-contact deflectometric measurement technique for surface and shape analysis of injection molds to facilitate deterministic surface quality control and to monitor minor conformity of the injection mold with the design data. The system is based on phase-measuring deflectometry with a operating measurement field of 80×80 mm(2) (±18° slope), a lateral resolution of 60μm and a local sensitivity of some nanometers. The calibration was tested with a calibration normal and a reference sphere. The results were crosschecked against a measurement of the same object with a tactile coordinate measuring machine. Eight injection molds for production of safety goggles with radii of +58mm (convex) and -60mm (concave) were measured in this study. The molds were separated into two groups (cavity 1 and 2 of the tool with different polishing techniques) and measured to test whether the measurement tool could extract differences. The analysis was performed on difference height between the measured surface and the spherical model. The device could derive the surface change due to polishing and discriminate between both polishing techniques, on the basis of the measured data. The concave nozzle sides of the first group (cavity 1) showed good shape conformity. In comparison, the nozzle sides of the second group (cavity 2) showed local deviations from design data up to 14.4μm. Local form variations of about 5μm occurred in the field of view. All convex ejector sides of both groups (cavity 1 and 2) showed rotational symmetric errors and the molds were measured in general flatter than design data. We applied a deflectometric system for measuring and evaluating specular reflective injection molding tools to optimize the production process of occupational eye wear. The surface quality could be inline monitored in the production processes for actual spectacle models. Copyright © 2013. Published by Elsevier GmbH.

Density-functional theory for internal magnetic fields

NASA Astrophysics Data System (ADS)

Tellgren, Erik I.

2018-01-01

A density-functional theory is developed based on the Maxwell-Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current density-functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis formulation of standard density-functional theory. Several variational principles as well as a Hohenberg-Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau-Yosida regularization) applied to the conventional Schrödinger ground-state energy, which imposes limits on the maximum curvature of the energy (with respect to the magnetic field) and enables construction of a (Fréchet) differentiable universal density functional.

Physical-geometric optics method for large size faceted particles.

PubMed

Sun, Bingqiang; Yang, Ping; Kattawar, George W; Zhang, Xiaodong

2017-10-02

A new physical-geometric optics method is developed to compute the single-scattering properties of faceted particles. It incorporates a general absorption vector to accurately account for inhomogeneous wave effects, and subsequently yields the relevant analytical formulas effective and computationally efficient for absorptive scattering particles. A bundle of rays incident on a certain facet can be traced as a single beam. For a beam incident on multiple facets, a systematic beam-splitting technique based on computer graphics is used to split the original beam into several sub-beams so that each sub-beam is incident only on an individual facet. The new beam-splitting technique significantly reduces the computational burden. The present physical-geometric optics method can be generalized to arbitrary faceted particles with either convex or concave shapes and with a homogeneous or an inhomogeneous (e.g., a particle with a core) composition. The single-scattering properties of irregular convex homogeneous and inhomogeneous hexahedra are simulated and compared to their counterparts from two other methods including a numerically rigorous method.

Optimization in Radiation Therapy: Applications in Brachytherapy and Intensity Modulated Radiation Therapy

NASA Astrophysics Data System (ADS)

McGeachy, Philip David

Over 50% of cancer patients require radiation therapy (RT). RT is an optimization problem requiring maximization of the radiation damage to the tumor while minimizing the harm to the healthy tissues. This dissertation focuses on two main RT optimization problems: 1) brachytherapy and 2) intensity modulated radiation therapy (IMRT). The brachytherapy research involved solving a non-convex optimization problem by creating an open-source genetic algorithm optimizer to determine the optimal radioactive seed distribution for a given set of patient volumes and constraints, both dosimetric- and implant-based. The optimizer was tested for a set of 45 prostate brachytherapy patients. While all solutions met the clinical standards, they also benchmarked favorably with those generated by a standard commercial solver. Compared to its compatriot, the salient features of the generated solutions were: slightly reduced prostate coverage, lower dose to the urethra and rectum, and a smaller number of needles required for an implant. Historically, IMRT requires modulation of fluence while keeping the photon beam energy fixed. The IMRT-related investigation in this thesis aimed at broadening the solution space by varying photon energy. The problem therefore involved simultaneous optimization of photon beamlet energy and fluence, denoted by XMRT. Formulating the problem as convex, linear programming was applied to obtain solutions for optimal energy-dependent fluences, while achieving all clinical objectives and constraints imposed. Dosimetric advantages of XMRT over single-energy IMRT in the improved sparing of organs at risk (OARs) was demonstrated in simplified phantom studies. The XMRT algorithm was improved to include clinical dose-volume constraints and clinical studies for prostate and head and neck cancer patients were investigated. Compared to IMRT, XMRT provided improved dosimetric benefit in the prostate case, particularly within intermediate- to low-dose regions (≤ 40 Gy) for OARs. For head and neck cases, XMRT solutions showed no significant disadvantage or advantage over IMRT. The deliverability concerns for the fluence maps generated from XMRT were addressed by incorporating smoothing constraints during the optimization and through successful generation of treatment machine files. Further research is needed to explore the full potential of the XMRT approach to RT.

Convex Lattice Polygons

ERIC Educational Resources Information Center

Scott, Paul

2006-01-01

A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.

New displacement-based methods for optimal truss topology design

NASA Technical Reports Server (NTRS)

Bendsoe, Martin P.; Ben-Tal, Aharon; Haftka, Raphael T.

1991-01-01

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

A note on resource allocation scheduling with group technology and learning effects on a single machine

NASA Astrophysics Data System (ADS)

Lu, Yuan-Yuan; Wang, Ji-Bo; Ji, Ping; He, Hongyu

2017-09-01

In this article, single-machine group scheduling with learning effects and convex resource allocation is studied. The goal is to find the optimal job schedule, the optimal group schedule, and resource allocations of jobs and groups. For the problem of minimizing the makespan subject to limited resource availability, it is proved that the problem can be solved in polynomial time under the condition that the setup times of groups are independent. For the general setup times of groups, a heuristic algorithm and a branch-and-bound algorithm are proposed, respectively. Computational experiments show that the performance of the heuristic algorithm is fairly accurate in obtaining near-optimal solutions.

A Brief Survey of Modern Optimization for Statisticians

PubMed Central

Lange, Kenneth; Chi, Eric C.; Zhou, Hua

2014-01-01

Modern computational statistics is turning more and more to high-dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include nondifferentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses a few important principles in algorithm design. Rather than view these principles in isolation, it is more productive to mix and match them. A few well chosen examples illustrate this point. Algorithm derivation is also emphasized, and theory is downplayed, particularly the abstractions of the convex calculus. Thus, our survey should be useful and accessible to a broad audience. PMID:25242858

In silico comparison of the reproducibility of full-arch implant provisional restorations to final restoration between a 3D Scan/CAD/CAM technique and the conventional method.

PubMed

Mino, Takuya; Maekawa, Kenji; Ueda, Akihiro; Higuchi, Shizuo; Sejima, Junichi; Takeuchi, Tetsuo; Hara, Emilio Satoshi; Kimura-Ono, Aya; Sonoyama, Wataru; Kuboki, Takuo

2015-04-01

The aim of this article was to investigate the accuracy in the reproducibility of full-arch implant provisional restorations to final restorations between a 3D Scan/CAD/CAM technique and the conventional method. We fabricated two final restorations for rehabilitation of maxillary and mandibular complete edentulous area and performed a computer-based comparative analysis of the accuracy in the reproducibility of the provisional restoration to final restoration between a 3D scanning and CAD/CAM (Scan/CAD/CAM) technique and the conventional silicone-mold transfer technique. Final restorations fabricated either by the conventional or Scan/CAD/CAM method were successfully installed in the patient. The total concave/convex volume discrepancy observed with the Scan/CAD/CAM technique was 503.50mm(3) and 338.15 mm(3) for maxillary and mandibular implant-supported prostheses (ISPs), respectively. On the other hand, total concave/convex volume discrepancy observed with the conventional method was markedly high (1106.84 mm(3) and 771.23 mm(3) for maxillary and mandibular ISPs, respectively). The results of the present report suggest that Scan/CAD/CAM method enables a more precise and accurate transfer of provisional restorations to final restorations compared to the conventional method. Copyright © 2014 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved.

Fabrication of complex free-standing nanostructures with concave and convex curvature via the layer-by-layer approach.

PubMed

Raoufi, Mohammad; Schönherr, Holger

2014-02-18

We report on the fabrication of unprecedented free-standing complex polymeric nanoobjects, which possess both concave and convex curvatures, by exploiting the layer-by-layer (LBL) deposition of polyelectrolytes. In a combined top-down/bottom-up replication approach pore diameter-modulated anodic aluminum oxide (AAO) templates, fabricated by temperature modulation hard anodization (TMHA), were replicated with multilayers of poly(styrene sulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) to yield open nanotubes with diameters in the wide and narrow segments of 210 and 150 nm, respectively. To obtain stable pore diameter-modulated nanopores, which possess segment lengths between 1 and 5 μm and 5 and 10 μm in the narrow and wide pore portion, respectively, conventional hard anodization of aluminum was followed by a subsequent temperature-modulated anodization. After removing the backside aluminum electrode, silanizing the aluminum oxide, and passivating the exposed membrane surface with a thin layer of gold, PSS and PAH were deposited alternatingly to yield LBL multilayers. For optimized LBL multilayer thicknesses and compactness, established in separate experiments on silicon substrates and nanoporous AAO with straight pores, free-standing polymeric nanoobjects with concave and convex curvatures, were obtained. These were stable for wall thickness to pore diameter ratios of ≥0.08.

Determining biosonar images using sparse representations.

PubMed

Fontaine, Bertrand; Peremans, Herbert

2009-05-01

Echolocating bats are thought to be able to create an image of their environment by emitting pulses and analyzing the reflected echoes. In this paper, the theory of sparse representations and its more recent further development into compressed sensing are applied to this biosonar image formation task. Considering the target image representation as sparse allows formulation of this inverse problem as a convex optimization problem for which well defined and efficient solution methods have been established. The resulting technique, referred to as L1-minimization, is applied to simulated data to analyze its performance relative to delay accuracy and delay resolution experiments. This method performs comparably to the coherent receiver for the delay accuracy experiments, is quite robust to noise, and can reconstruct complex target impulse responses as generated by many closely spaced reflectors with different reflection strengths. This same technique, in addition to reconstructing biosonar target images, can be used to simultaneously localize these complex targets by interpreting location cues induced by the bat's head related transfer function. Finally, a tentative explanation is proposed for specific bat behavioral experiments in terms of the properties of target images as reconstructed by the L1-minimization method.

Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Zhang, Han; Chen, Xuefeng; Du, Zhaohui; Yan, Ruqiang

2016-12-01

The bearing failure, generating harmful vibrations, is one of the most frequent reasons for machine breakdowns. Thus, performing bearing fault diagnosis is an essential procedure to improve the reliability of the mechanical system and reduce its operating expenses. Most of the previous studies focused on rolling bearing fault diagnosis could be categorized into two main families, kurtosis-based filter method and wavelet-based shrinkage method. Although tremendous progresses have been made, their effectiveness suffers from three potential drawbacks: firstly, fault information is often decomposed into proximal frequency bands and results in impulsive feature frequency band splitting (IFFBS) phenomenon, which significantly degrades the performance of capturing the optimal information band; secondly, noise energy spreads throughout all frequency bins and contaminates fault information in the information band, especially under the heavy noisy circumstance; thirdly, wavelet coefficients are shrunk equally to satisfy the sparsity constraints and most of the feature information energy are thus eliminated unreasonably. Therefore, exploiting two pieces of prior information (i.e., one is that the coefficient sequences of fault information in the wavelet basis is sparse, and the other is that the kurtosis of the envelope spectrum could evaluate accurately the information capacity of rolling bearing faults), a novel weighted sparse model and its corresponding framework for bearing fault diagnosis is proposed in this paper, coined KurWSD. KurWSD formulates the prior information into weighted sparse regularization terms and then obtains a nonsmooth convex optimization problem. The alternating direction method of multipliers (ADMM) is sequentially employed to solve this problem and the fault information is extracted through the estimated wavelet coefficients. Compared with state-of-the-art methods, KurWSD overcomes the three drawbacks and utilizes the advantages of both family tools. KurWSD has three main advantages: firstly, all the characteristic information scattered in proximal sub-bands is gathered through synthesizing those impulsive dominant sub-band signals and thus eliminates the dilemma of the IFFBS phenomenon. Secondly, the noises in the focused sub-bands could be alleviated efficiently through shrinking or removing the dense wavelet coefficients of Gaussian noise. Lastly, wavelet coefficients with faulty information are reliably detected and preserved through manipulating wavelet coefficients discriminatively based on the contribution to the impulsive components. Moreover, the reliability and effectiveness of the KurWSD are demonstrated through simulated and experimental signals.

Antireflective surface with a step in the taper: Numerical optimization and large-area fabrication

NASA Astrophysics Data System (ADS)

Shinotsuka, Kei; Hongo, Koki; Dai, Kotaro; Hirama, Satoru; Hatta, Yoshihisa

2017-02-01

In this study, we developed a practical method to improve the optical performance of subwavelength antireflective two-dimensional (2D) gratings. A numerical simulation of both convex and concave paraboloids suggested that surface reflectivity drastically decreases when a step is introduced in the taper. The optimum height and depth of a step provided average reflectances of 0.098% for convex protrusions and 0.040% for concave protrusions in the visible range. Furthermore, a stepped paraboloid was experimentally fabricated by dry etching of a Si substrate with SiO2 particle monolayer mask. A cyclo-olefin polymer (COP) reverse replica (concave) imprinted by the Si mold exhibited a measured reflectance of 0.077% on average in the visible range. It was also demonstrated that the antireflective structure was fabricated on the whole surface of a 6 in. Si wafer, which is a sufficient size for industrial utilization.

Origami silicon optoelectronics for hemispherical electronic eye systems.

PubMed

Zhang, Kan; Jung, Yei Hwan; Mikael, Solomon; Seo, Jung-Hun; Kim, Munho; Mi, Hongyi; Zhou, Han; Xia, Zhenyang; Zhou, Weidong; Gong, Shaoqin; Ma, Zhenqiang

2017-11-24

Digital image sensors in hemispherical geometries offer unique imaging advantages over their planar counterparts, such as wide field of view and low aberrations. Deforming miniature semiconductor-based sensors with high-spatial resolution into such format is challenging. Here we report a simple origami approach for fabricating single-crystalline silicon-based focal plane arrays and artificial compound eyes that have hemisphere-like structures. Convex isogonal polyhedral concepts allow certain combinations of polygons to fold into spherical formats. Using each polygon block as a sensor pixel, the silicon-based devices are shaped into maps of truncated icosahedron and fabricated on flexible sheets and further folded either into a concave or convex hemisphere. These two electronic eye prototypes represent simple and low-cost methods as well as flexible optimization parameters in terms of pixel density and design. Results demonstrated in this work combined with miniature size and simplicity of the design establish practical technology for integration with conventional electronic devices.

Resource allocation for error resilient video coding over AWGN using optimization approach.

PubMed

An, Cheolhong; Nguyen, Truong Q

2008-12-01

The number of slices for error resilient video coding is jointly optimized with 802.11a-like media access control and the physical layers with automatic repeat request and rate compatible punctured convolutional code over additive white gaussian noise channel as well as channel times allocation for time division multiple access. For error resilient video coding, the relation between the number of slices and coding efficiency is analyzed and formulated as a mathematical model. It is applied for the joint optimization problem, and the problem is solved by a convex optimization method such as the primal-dual decomposition method. We compare the performance of a video communication system which uses the optimal number of slices with one that codes a picture as one slice. From numerical examples, end-to-end distortion of utility functions can be significantly reduced with the optimal slices of a picture especially at low signal-to-noise ratio.

Joint Optimization of Receiver Placement and Illuminator Selection for a Multiband Passive Radar Network.

PubMed

Xie, Rui; Wan, Xianrong; Hong, Sheng; Yi, Jianxin

2017-06-14

The performance of a passive radar network can be greatly improved by an optimal radar network structure. Generally, radar network structure optimization consists of two aspects, namely the placement of receivers in suitable places and selection of appropriate illuminators. The present study investigates issues concerning the joint optimization of receiver placement and illuminator selection for a passive radar network. Firstly, the required radar cross section (RCS) for target detection is chosen as the performance metric, and the joint optimization model boils down to the partition p -center problem (PPCP). The PPCP is then solved by a proposed bisection algorithm. The key of the bisection algorithm lies in solving the partition set covering problem (PSCP), which can be solved by a hybrid algorithm developed by coupling the convex optimization with the greedy dropping algorithm. In the end, the performance of the proposed algorithm is validated via numerical simulations.

Intelligent Distributed Systems

DTIC Science & Technology

2015-10-23

periodic gossiping algorithms by using convex combination rules rather than standard averaging rules. On a ring graph, we have discovered how to sequence...the gossips within a period to achieve the best possible convergence rate and we have related this optimal value to the classic edge coloring problem...consensus. There are three different approaches to distributed averaging: linear iterations, gossiping , and dou- ble linear iterations which are also known as

A Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

DTIC Science & Technology

2012-08-01

model appears in cosmic microwave background analysis [10] which solves min A,Y λ 2 trace ( (ABY − X)>C−1(ABY − X) ) + r(Y), subject to A ∈ D (1.5...and “×n” represent outer product and tensor-matrix multiplication, respectively. (The necessary background of tensor is reviewed in Sec. 3) Most

Generalized bipartite quantum state discrimination problems with sequential measurements

NASA Astrophysics Data System (ADS)

Nakahira, Kenji; Kato, Kentaro; Usuda, Tsuyoshi Sasaki

2018-02-01

We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only local operations and one-way classical communication are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. Our results are applicable to various practical optimization criteria, including the Bayes criterion, the Neyman-Pearson criterion, and the minimax criterion. In the setting of the problem of finding an optimal global measurement, its dual problem and necessary and sufficient conditions for an optimal solution have been widely used to obtain analytical and numerical expressions for optimal solutions. Similarly, our results are useful to obtain analytical and numerical expressions for optimal sequential measurements. Examples in which our results can be used to obtain an analytical expression for an optimal sequential measurement are provided.

Estimating 3D positions and velocities of projectiles from monocular views.

PubMed

Ribnick, Evan; Atev, Stefan; Papanikolopoulos, Nikolaos P

2009-05-01

In this paper, we consider the problem of localizing a projectile in 3D based on its apparent motion in a stationary monocular view. A thorough theoretical analysis is developed, from which we establish the minimum conditions for the existence of a unique solution. The theoretical results obtained have important implications for applications involving projectile motion. A robust, nonlinear optimization-based formulation is proposed, and the use of a local optimization method is justified by detailed examination of the local convexity structure of the cost function. The potential of this approach is validated by experimental results.

Thermal lens effect for optimizing a passively Q-switched 1064 nm laser

NASA Astrophysics Data System (ADS)

Xing, Enbo; Rong, Jiamin; Khew, Si Ying; Tong, Cunzhu; Hong, Minghui

2018-06-01

We demonstrate the improvement of pulse characteristics of a passively Q-switched laser by utilizing the thermal lens effect of a saturable absorber (SA) inside the cavity. The experimental results show that the SA should be considered as a convex lens inside the cavity, whose position strongly improves output performance. A fourfold enhancement of the average output power is obtained, and the peak energy increases from 8.2 to 25 µJ. Theoretically, we calculate the thermal lens effect of the SA and the optimal position inside the cavity, which agree with the experimental results.

Variational Quantum Tomography with Incomplete Information by Means of Semidefinite Programs

NASA Astrophysics Data System (ADS)

Maciel, Thiago O.; Cesário, André T.; Vianna, Reinaldo O.

We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar to compressed sensing approaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort corresponding to an informationally complete measurement.

Feedback-Based Projected-Gradient Method for Real-Time Optimization of Aggregations of Energy Resources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Bernstein, Andrey; Simonetto, Andrea

This paper develops an online optimization method to maximize operational objectives of distribution-level distributed energy resources (DERs), while adjusting the aggregate power generated (or consumed) in response to services requested by grid operators. The design of the online algorithm is based on a projected-gradient method, suitably modified to accommodate appropriate measurements from the distribution network and the DERs. By virtue of this approach, the resultant algorithm can cope with inaccuracies in the representation of the AC power flows, it avoids pervasive metering to gather the state of noncontrollable resources, and it naturally lends itself to a distributed implementation. Optimality claimsmore » are established in terms of tracking of the solution of a well-posed time-varying convex optimization problem.« less

Comparing a Coevolutionary Genetic Algorithm for Multiobjective Optimization

NASA Technical Reports Server (NTRS)

Lohn, Jason D.; Kraus, William F.; Haith, Gary L.; Clancy, Daniel (Technical Monitor)

2002-01-01

We present results from a study comparing a recently developed coevolutionary genetic algorithm (CGA) against a set of evolutionary algorithms using a suite of multiobjective optimization benchmarks. The CGA embodies competitive coevolution and employs a simple, straightforward target population representation and fitness calculation based on developmental theory of learning. Because of these properties, setting up the additional population is trivial making implementation no more difficult than using a standard GA. Empirical results using a suite of two-objective test functions indicate that this CGA performs well at finding solutions on convex, nonconvex, discrete, and deceptive Pareto-optimal fronts, while giving respectable results on a nonuniform optimization. On a multimodal Pareto front, the CGA finds a solution that dominates solutions produced by eight other algorithms, yet the CGA has poor coverage across the Pareto front.

Source term identification in atmospheric modelling via sparse optimization

NASA Astrophysics Data System (ADS)

Adam, Lukas; Branda, Martin; Hamburger, Thomas

2015-04-01

Inverse modelling plays an important role in identifying the amount of harmful substances released into atmosphere during major incidents such as power plant accidents or volcano eruptions. Another possible application of inverse modelling lies in the monitoring the CO2 emission limits where only observations at certain places are available and the task is to estimate the total releases at given locations. This gives rise to minimizing the discrepancy between the observations and the model predictions. There are two standard ways of solving such problems. In the first one, this discrepancy is regularized by adding additional terms. Such terms may include Tikhonov regularization, distance from a priori information or a smoothing term. The resulting, usually quadratic, problem is then solved via standard optimization solvers. The second approach assumes that the error term has a (normal) distribution and makes use of Bayesian modelling to identify the source term. Instead of following the above-mentioned approaches, we utilize techniques from the field of compressive sensing. Such techniques look for a sparsest solution (solution with the smallest number of nonzeros) of a linear system, where a maximal allowed error term may be added to this system. Even though this field is a developed one with many possible solution techniques, most of them do not consider even the simplest constraints which are naturally present in atmospheric modelling. One of such examples is the nonnegativity of release amounts. We believe that the concept of a sparse solution is natural in both problems of identification of the source location and of the time process of the source release. In the first case, it is usually assumed that there are only few release points and the task is to find them. In the second case, the time window is usually much longer than the duration of the actual release. In both cases, the optimal solution should contain a large amount of zeros, giving rise to the concept of sparsity. In the paper, we summarize several optimization techniques which are used for finding sparse solutions and propose their modifications to handle selected constraints such as nonnegativity constraints and simple linear constraints, for example the minimal or maximal amount of total release. These techniques range from successive convex approximations to solution of one nonconvex problem. On simple examples, we explain these techniques and compare them from the point of implementation simplicity, approximation capability and convergence properties. Finally, these methods will be applied on the European Tracer Experiment (ETEX) data and the results will be compared with the current state of arts techniques such as regularized least squares or Bayesian approach. The obtained results show the surprisingly good results of these techniques. This research is supported by EEA/Norwegian Financial Mechanism under project 7F14287 STRADI.

Posterior spinal fusion for adolescent idiopathic scoliosis using a convex pedicle screw technique: a novel concept of deformity correction.

PubMed

Tsirikos, A I; Mataliotakis, G; Bounakis, N

2017-08-01

We present the results of correcting a double or triple curve adolescent idiopathic scoliosis using a convex segmental pedicle screw technique. We reviewed 191 patients with a mean age at surgery of 15 years (11 to 23.3). Pedicle screws were placed at the convexity of each curve. Concave screws were inserted at one or two cephalad levels and two caudal levels. The mean operating time was 183 minutes (132 to 276) and the mean blood loss 0.22% of the total blood volume (0.08% to 0.4%). Multimodal monitoring remained stable throughout the operation. The mean hospital stay was 6.8 days (5 to 15). The mean post-operative follow-up was 5.8 years (2.5 to 9.5). There were no neurological complications, deep wound infection, obvious nonunion or need for revision surgery. Upper thoracic scoliosis was corrected by a mean 68.2% (38% to 48%, p < 0.001). Main thoracic scoliosis was corrected by a mean 71% (43.5% to 8.9%, p < 0.001). Lumbar scoliosis was corrected by a mean 72.3% (41% to 90%, p < 0.001). No patient lost more than 3° of correction at follow-up. The thoracic kyphosis improved by 13.1° (-21° to 49°, p < 0.001); the lumbar lordosis remained unchanged (p = 0.58). Coronal imbalance was corrected by a mean 98% (0% to 100%, p < 0.001). Sagittal imbalance was corrected by a mean 96% (20% to 100%, p < 0.001). The Scoliosis Research Society Outcomes Questionnaire score improved from a mean 3.6 to 4.6 (2.4 to 4, p < 0.001); patient satisfaction was a mean 4.9 (4.8 to 5). This technique carries low neurological and vascular risks because the screws are placed in the pedicles of the convex side of the curve, away from the spinal cord, cauda equina and the aorta. A low implant density (pedicle screw density 1.2, when a density of 2 represents placement of pedicle screws bilaterally at every instrumented segment) achieved satisfactory correction of the scoliosis, an improved thoracic kyphosis and normal global sagittal balance. Both patient satisfaction and functional outcomes were excellent. Cite this article: Bone Joint J 2017;99-B:1080-7. ©2017 The British Editorial Society of Bone & Joint Surgery.

Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses

PubMed Central

Schein, Stan; Gayed, James Maurice

2014-01-01

The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry––tetrahedral, octahedral, and icosahedral––are the 5 Platonic polyhedra, the 13 Archimedean polyhedra––including the truncated icosahedron or soccer ball––and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, “Goldberg polyhedra,” which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a “Goldberg triangle.” We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler’s rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry. PMID:24516137

Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses.

PubMed

Schein, Stan; Gayed, James Maurice

2014-02-25

The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry--tetrahedral, octahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry.

Problem Solving Techniques for the Design of Algorithms.

ERIC Educational Resources Information Center

Kant, Elaine; Newell, Allen

1984-01-01

Presents model of algorithm design (activity in software development) based on analysis of protocols of two subjects designing three convex hull algorithms. Automation methods, methods for studying algorithm design, role of discovery in problem solving, and comparison of different designs of case study according to model are highlighted.…

CONVEX mini manual

NASA Technical Reports Server (NTRS)

Tennille, Geoffrey M.; Howser, Lona M.

1993-01-01

The use of the CONVEX computers that are an integral part of the Supercomputing Network Subsystems (SNS) of the Central Scientific Computing Complex of LaRC is briefly described. Features of the CONVEX computers that are significantly different than the CRAY supercomputers are covered, including: FORTRAN, C, architecture of the CONVEX computers, the CONVEX environment, batch job submittal, debugging, performance analysis, utilities unique to CONVEX, and documentation. This revision reflects the addition of the Applications Compiler and X-based debugger, CXdb. The document id intended for all CONVEX users as a ready reference to frequently asked questions and to more detailed information contained with the vendor manuals. It is appropriate for both the novice and the experienced user.

Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention.

PubMed

Bertamini, Marco; Wagemans, Johan

2013-04-01

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

Extended surface parallel coating inspection method

DOEpatents

Naulleau, Patrick P.

2006-03-21

Techniques for rapidly characterizing reflective surfaces and especially multi-layer EUV reflective surfaces of optical components involve illuminating the entire reflective surface instantaneously and detecting the image far field. The technique provides a mapping of points on the reflective surface to corresponding points on a detector, e.g., CCD. This obviates the need to scan a probe over the entire surface of the optical component. The reflective surface can be flat, convex, or concave.

Super-resolution for scanning light stimulation systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bitzer, L. A.; Neumann, K.; Benson, N., E-mail: niels.benson@uni-due.de

Super-resolution (SR) is a technique used in digital image processing to overcome the resolution limitation of imaging systems. In this process, a single high resolution image is reconstructed from multiple low resolution images. SR is commonly used for CCD and CMOS (Complementary Metal-Oxide-Semiconductor) sensor images, as well as for medical applications, e.g., magnetic resonance imaging. Here, we demonstrate that super-resolution can be applied with scanning light stimulation (LS) systems, which are common to obtain space-resolved electro-optical parameters of a sample. For our purposes, the Projection Onto Convex Sets (POCS) was chosen and modified to suit the needs of LS systems.more » To demonstrate the SR adaption, an Optical Beam Induced Current (OBIC) LS system was used. The POCS algorithm was optimized by means of OBIC short circuit current measurements on a multicrystalline solar cell, resulting in a mean square error reduction of up to 61% and improved image quality.« less

Long-range depth profiling of camouflaged targets using single-photon detection

NASA Astrophysics Data System (ADS)

Tobin, Rachael; Halimi, Abderrahim; McCarthy, Aongus; Ren, Ximing; McEwan, Kenneth J.; McLaughlin, Stephen; Buller, Gerald S.

2018-03-01

We investigate the reconstruction of depth and intensity profiles from data acquired using a custom-designed time-of-flight scanning transceiver based on the time-correlated single-photon counting technique. The system had an operational wavelength of 1550 nm and used a Peltier-cooled InGaAs/InP single-photon avalanche diode detector. Measurements were made of human figures, in plain view and obscured by camouflage netting, from a stand-off distance of 230 m in daylight using only submilliwatt average optical powers. These measurements were analyzed using a pixelwise cross correlation approach and compared to analysis using a bespoke algorithm designed for the restoration of multilayered three-dimensional light detection and ranging images. This algorithm is based on the optimization of a convex cost function composed of a data fidelity term and regularization terms, and the results obtained show that it achieves significant improvements in image quality for multidepth scenarios and for reduced acquisition times.

Mathematical analysis on the cosets of subgroup in the group of E-convex sets

NASA Astrophysics Data System (ADS)

Abbas, Nada Mohammed; Ajeena, Ruma Kareem K.

2018-05-01

In this work, analyzing the cosets of the subgroup in the group of L – convex sets is presented as a new and powerful tool in the topics of the convex analysis and abstract algebra. On L – convex sets, the properties of these cosets are proved mathematically. Most important theorem on a finite group of L – convex sets theory which is the Lagrange’s Theorem has been proved. As well as, the mathematical proof of the quotient group of L – convex sets is presented.

Heat Transfer Search Algorithm for Non-convex Economic Dispatch Problems

NASA Astrophysics Data System (ADS)

Hazra, Abhik; Das, Saborni; Basu, Mousumi

2018-06-01

This paper presents Heat Transfer Search (HTS) algorithm for the non-linear economic dispatch problem. HTS algorithm is based on the law of thermodynamics and heat transfer. The proficiency of the suggested technique has been disclosed on three dissimilar complicated economic dispatch problems with valve point effect; prohibited operating zone; and multiple fuels with valve point effect. Test results acquired from the suggested technique for the economic dispatch problem have been fitted to that acquired from other stated evolutionary techniques. It has been observed that the suggested HTS carry out superior solutions.

Heat Transfer Search Algorithm for Non-convex Economic Dispatch Problems

NASA Astrophysics Data System (ADS)

Hazra, Abhik; Das, Saborni; Basu, Mousumi

2018-03-01

This paper presents Heat Transfer Search (HTS) algorithm for the non-linear economic dispatch problem. HTS algorithm is based on the law of thermodynamics and heat transfer. The proficiency of the suggested technique has been disclosed on three dissimilar complicated economic dispatch problems with valve point effect; prohibited operating zone; and multiple fuels with valve point effect. Test results acquired from the suggested technique for the economic dispatch problem have been fitted to that acquired from other stated evolutionary techniques. It has been observed that the suggested HTS carry out superior solutions.

SU-E-T-549: A Combinatorial Optimization Approach to Treatment Planning with Non-Uniform Fractions in Intensity Modulated Proton Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Papp, D; Unkelbach, J

2014-06-01

Purpose: Non-uniform fractionation, i.e. delivering distinct dose distributions in two subsequent fractions, can potentially improve outcomes by increasing biological dose to the target without increasing dose to healthy tissues. This is possible if both fractions deliver a similar dose to normal tissues (exploit the fractionation effect) but high single fraction doses to subvolumes of the target (hypofractionation). Optimization of such treatment plans can be formulated using biological equivalent dose (BED), but leads to intractable nonconvex optimization problems. We introduce a novel optimization approach to address this challenge. Methods: We first optimize a reference IMPT plan using standard techniques that deliversmore » a homogeneous target dose in both fractions. The method then divides the pencil beams into two sets, which are assigned to either fraction one or fraction two. The total intensity of each pencil beam, and therefore the physical dose, remains unchanged compared to the reference plan. The objectives are to maximize the mean BED in the target and to minimize the mean BED in normal tissues, which is a quadratic function of the pencil beam weights. The optimal reassignment of pencil beams to one of the two fractions is formulated as a binary quadratic optimization problem. A near-optimal solution to this problem can be obtained by convex relaxation and randomized rounding. Results: The method is demonstrated for a large arteriovenous malformation (AVM) case treated in two fractions. The algorithm yields a treatment plan, which delivers a high dose to parts of the AVM in one of the fractions, but similar doses in both fractions to the normal brain tissue adjacent to the AVM. Using the approach, the mean BED in the target was increased by approximately 10% compared to what would have been possible with a uniform reference plan for the same normal tissue mean BED.« less

The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.

PubMed

Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie

2016-01-01

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).

On Data Transfers Over Wide-Area Dedicated Connections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rao, Nageswara S.; Liu, Qiang

Dedicated wide-area network connections are employed in big data and high-performance computing scenarios, since the absence of cross-traffic promises to make it easier to analyze and optimize data transfers over them. However, nonlinear transport dynamics and end-system complexity due to multi-core hosts and distributed file systems make these tasks surprisingly challenging. We present an overview of methods to analyze memory and disk file transfers using extensive measurements over 10 Gbps physical and emulated connections with 0–366 ms round trip times (RTTs). For memory transfers, we derive performance profiles of TCP and UDT throughput as a function of RTT, which showmore » concave regions in contrast to entirely convex regions predicted by previous models. These highly desirable concave regions can be expanded by utilizing large buffers and more parallel flows. We also present Poincar´e maps and Lyapunov exponents of TCP and UDT throughputtraces that indicate complex throughput dynamics. For disk file transfers, we show that throughput can be optimized using a combination of parallel I/O and network threads under direct I/O mode. Our initial throughput measurements of Lustre filesystems mounted over long-haul connections using LNet routers show convex profiles indicative of I/O limits.« less

Chromatically corrected virtual image visual display. [reducing eye strain in flight simulators

NASA Technical Reports Server (NTRS)

Kahlbaum, W. M., Jr. (Inventor)

1980-01-01

An in-line, three element, large diameter, optical display lens is disclosed which has a front convex-convex element, a central convex-concave element, and a rear convex-convex element. The lens, used in flight simulators, magnifies an image presented on a television monitor and, by causing light rays leaving the lens to be in essentially parallel paths, reduces eye strain of the simulator operator.

Design and optimization of color lookup tables on a simplex topology.

PubMed

Monga, Vishal; Bala, Raja; Mo, Xuan

2012-04-01

An important computational problem in color imaging is the design of color transforms that map color between devices or from a device-dependent space (e.g., RGB/CMYK) to a device-independent space (e.g., CIELAB) and vice versa. Real-time processing constraints entail that such nonlinear color transforms be implemented using multidimensional lookup tables (LUTs). Furthermore, relatively sparse LUTs (with efficient interpolation) are employed in practice because of storage and memory constraints. This paper presents a principled design methodology rooted in constrained convex optimization to design color LUTs on a simplex topology. The use of n simplexes, i.e., simplexes in n dimensions, as opposed to traditional lattices, recently has been of great interest in color LUT design for simplex topologies that allow both more analytically tractable formulations and greater efficiency in the LUT. In this framework of n-simplex interpolation, our central contribution is to develop an elegant iterative algorithm that jointly optimizes the placement of nodes of the color LUT and the output values at those nodes to minimize interpolation error in an expected sense. This is in contrast to existing work, which exclusively designs either node locations or the output values. We also develop new analytical results for the problem of node location optimization, which reduces to constrained optimization of a large but sparse interpolation matrix in our framework. We evaluate our n -simplex color LUTs against the state-of-the-art lattice (e.g., International Color Consortium profiles) and simplex-based techniques for approximating two representative multidimensional color transforms that characterize a CMYK xerographic printer and an RGB scanner, respectively. The results show that color LUTs designed on simplexes offer very significant benefits over traditional lattice-based alternatives in improving color transform accuracy even with a much smaller number of nodes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiribella, G.; D'Ariano, G. M.; Perinotti, P.

We investigate the problem of cloning a set of states that is invariant under the action of an irreducible group representation. We then characterize the cloners that are extremal in the convex set of group covariant cloning machines, among which one can restrict the search for optimal cloners. For a set of states that is invariant under the discrete Weyl-Heisenberg group, we show that all extremal cloners can be unitarily realized using the so-called double-Bell states, whence providing a general proof of the popular ansatz used in the literature for finding optimal cloners in a variety of settings. Our resultmore » can also be generalized to continuous-variable optimal cloning in infinite dimensions, where the covariance group is the customary Weyl-Heisenberg group of displacement000.« less

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles R.

2018-02-01

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.

Scoliosis convexity and organ anatomy are related.

PubMed

Schlösser, Tom P C; Semple, Tom; Carr, Siobhán B; Padley, Simon; Loebinger, Michael R; Hogg, Claire; Castelein, René M

2017-06-01

Primary ciliary dyskinesia (PCD) is a respiratory syndrome in which 'random' organ orientation can occur; with approximately 46% of patients developing situs inversus totalis at organogenesis. The aim of this study was to explore the relationship between organ anatomy and curve convexity by studying the prevalence and convexity of idiopathic scoliosis in PCD patients with and without situs inversus. Chest radiographs of PCD patients were systematically screened for existence of significant lateral spinal deviation using the Cobb angle. Positive values represented right-sided convexity. Curve convexity and Cobb angles were compared between PCD patients with situs inversus and normal anatomy. A total of 198 PCD patients were screened. The prevalence of scoliosis (Cobb >10°) and significant spinal asymmetry (Cobb 5-10°) was 8 and 23%, respectively. Curve convexity and Cobb angle were significantly different within both groups between situs inversus patients and patients with normal anatomy (P ≤ 0.009). Moreover, curve convexity correlated significantly with organ orientation (P < 0.001; ϕ = 0.882): In 16 PCD patients with scoliosis (8 situs inversus and 8 normal anatomy), except for one case, matching of curve convexity and orientation of organ anatomy was observed: convexity of the curve was opposite to organ orientation. This study supports our hypothesis on the correlation between organ anatomy and curve convexity in scoliosis: the convexity of the thoracic curve is predominantly to the right in PCD patients that were 'randomized' to normal organ anatomy and to the left in patients with situs inversus totalis.

Geosynchronous earth orbit/low earth orbit space object inspection and debris disposal: A preliminary analysis using a carrier satellite with deployable small satellites

NASA Astrophysics Data System (ADS)

Crockett, Derick

Detailed observations of geosynchronous satellites from earth are very limited. To better inspect these high altitude satellites, the use of small, refuelable satellites is proposed. The small satellites are stationed on a carrier platform in an orbit near the population of geosynchronous satellites. A carrier platform equipped with deployable, refuelable SmallSats is a viable option to inspect geosynchronous satellites. The propellant requirement to transfer to a targeted geosynchronous satellite, perform a proximity inspection mission, and transfer back to the carrier platform in a nearby orbit is determined. Convex optimization and traditional optimization techniques are explored, determining minimum propellant trajectories. Propellant is measured by the total required change in velocity, delta-v. The trajectories were modeled in a relative reference frame using the Clohessy-Wiltshire equations. Mass estimations for the carrier platform and the SmallSat were determined by using the rocket equation. The mass estimates were compared to the mass of a single, non-refuelable satellite performing the same geosynchronous satellite inspection missions. From the minimum delta-v trajectories and the mass analysis, it is determined that using refuelable SmallSats and a carrier platform in a nearby orbit can be more efficient than using a single non-refuelable satellite to perform multiple geosynchronous satellite inspections.

Randomized algorithms for high quality treatment planning in volumetric modulated arc therapy

NASA Astrophysics Data System (ADS)

Yang, Yu; Dong, Bin; Wen, Zaiwen

2017-02-01

In recent years, volumetric modulated arc therapy (VMAT) has been becoming a more and more important radiation technique widely used in clinical application for cancer treatment. One of the key problems in VMAT is treatment plan optimization, which is complicated due to the constraints imposed by the involved equipments. In this paper, we consider a model with four major constraints: the bound on the beam intensity, an upper bound on the rate of the change of the beam intensity, the moving speed of leaves of the multi-leaf collimator (MLC) and its directional-convexity. We solve the model by a two-stage algorithm: performing minimization with respect to the shapes of the aperture and the beam intensities alternatively. Specifically, the shapes of the aperture are obtained by a greedy algorithm whose performance is enhanced by random sampling in the leaf pairs with a decremental rate. The beam intensity is optimized using a gradient projection method with non-monotonic line search. We further improve the proposed algorithm by an incremental random importance sampling of the voxels to reduce the computational cost of the energy functional. Numerical simulations on two clinical cancer date sets demonstrate that our method is highly competitive to the state-of-the-art algorithms in terms of both computational time and quality of treatment planning.

Local classifier weighting by quadratic programming.

PubMed

Cevikalp, Hakan; Polikar, Robi

2008-10-01

It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space.

Use of Convexity in Ostomy Care

PubMed Central

Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel

2017-01-01

Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes. PMID:28002174

Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhao, Changhong; Zamzam, Admed S.

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successivemore » convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.« less

The effects of a convex rear-view mirror on ocular accommodative responses.

PubMed

Nagata, Tatsuo; Iwasaki, Tsuneto; Kondo, Hiroyuki; Tawara, Akihiko

2013-11-01

Convex mirrors are universally used as rear-view mirrors in automobiles. However, the ocular accommodative responses during the use of these mirrors have not yet been examined. This study investigated the effects of a convex mirror on the ocular accommodative systems. Seven young adults with normal visual functions were ordered to binocularly watch an object in a convex or plane mirror. The accommodative responses were measured with an infrared optometer. The average of the accommodation of all subjects while viewing the object in the convex mirror were significantly nearer than in the plane mirror, although all subjects perceived the position of the object in the convex mirror as being farther away. Moreover, the fluctuations of accommodation were significantly larger for the convex mirror. The convex mirror caused the 'false recognition of distance', which induced the large accommodative fluctuations and blurred vision. Manufactures should consider the ocular accommodative responses as a new indicator for increasing automotive safety. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

Statistical Optimality in Multipartite Ranking and Ordinal Regression.

PubMed

Uematsu, Kazuki; Lee, Yoonkyung

2015-05-01

Statistical optimality in multipartite ranking is investigated as an extension of bipartite ranking. We consider the optimality of ranking algorithms through minimization of the theoretical risk which combines pairwise ranking errors of ordinal categories with differential ranking costs. The extension shows that for a certain class of convex loss functions including exponential loss, the optimal ranking function can be represented as a ratio of weighted conditional probability of upper categories to lower categories, where the weights are given by the misranking costs. This result also bridges traditional ranking methods such as proportional odds model in statistics with various ranking algorithms in machine learning. Further, the analysis of multipartite ranking with different costs provides a new perspective on non-smooth list-wise ranking measures such as the discounted cumulative gain and preference learning. We illustrate our findings with simulation study and real data analysis.

Boattail juncture shaping for spin-stabilized rounds in supersonic flight

NASA Astrophysics Data System (ADS)

Jiajan, W.; Chue, R. S. M.; Nguyen, T.; Yu, S. C. M.

2015-03-01

In this paper, the effects of boattail junction shaping on aerodynamic drag and stability of supersonic spin-stabilized rounds are investigated using computational fluid dynamics. For a generic round body comprising of a secant-ogive nose, a cylindrical body and a conical boattail, the shaping technique was achieved by adding a convex surface of varying degrees of radius of curvature to the junction between the cylindrical body and the boattail. It was shown through numerical simulations that this shaping technique can provide a reduction in aerodynamic drag of up to 5.4 % without destabilizing the round bodies when the radius of curvature is less than 8.8 times the diameter of the cylindrical body. The more gradual change of the flow characteristics, e.g., the pressure over the convex surface, was identified as the main reason for the drag reduction. A unique aspect of the current work is that stability is treated as an integral part of the performance assessment. It was also found that the dynamic instability encountered at large radii of curvature is due to the Magnus effects.

Revisiting separation properties of convex fuzzy sets

USDA-ARS?s Scientific Manuscript database

Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointne...

Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System.

PubMed

Chinnadurai, Sunil; Selvaprabhu, Poongundran; Jeong, Yongchae; Jiang, Xueqin; Lee, Moon Ho

2017-09-18

In this paper, we examine the robust beamforming design to tackle the energy efficiency (EE) maximization problem in a 5G massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) downlink system with imperfect channel state information (CSI) at the base station. A novel joint user pairing and dynamic power allocation (JUPDPA) algorithm is proposed to minimize the inter user interference and also to enhance the fairness between the users. This work assumes imperfect CSI by adding uncertainties to channel matrices with worst-case model, i.e., ellipsoidal uncertainty model (EUM). A fractional non-convex optimization problem is formulated to maximize the EE subject to the transmit power constraints and the minimum rate requirement for the cell edge user. The designed problem is difficult to solve due to its nonlinear fractional objective function. We firstly employ the properties of fractional programming to transform the non-convex problem into its equivalent parametric form. Then, an efficient iterative algorithm is proposed established on the constrained concave-convex procedure (CCCP) that solves and achieves convergence to a stationary point of the above problem. Finally, Dinkelbach's algorithm is employed to determine the maximum energy efficiency. Comprehensive numerical results illustrate that the proposed scheme attains higher worst-case energy efficiency as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.

Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System

PubMed Central

Jeong, Yongchae; Jiang, Xueqin; Lee, Moon Ho

2017-01-01

In this paper, we examine the robust beamforming design to tackle the energy efficiency (EE) maximization problem in a 5G massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) downlink system with imperfect channel state information (CSI) at the base station. A novel joint user pairing and dynamic power allocation (JUPDPA) algorithm is proposed to minimize the inter user interference and also to enhance the fairness between the users. This work assumes imperfect CSI by adding uncertainties to channel matrices with worst-case model, i.e., ellipsoidal uncertainty model (EUM). A fractional non-convex optimization problem is formulated to maximize the EE subject to the transmit power constraints and the minimum rate requirement for the cell edge user. The designed problem is difficult to solve due to its nonlinear fractional objective function. We firstly employ the properties of fractional programming to transform the non-convex problem into its equivalent parametric form. Then, an efficient iterative algorithm is proposed established on the constrained concave-convex procedure (CCCP) that solves and achieves convergence to a stationary point of the above problem. Finally, Dinkelbach’s algorithm is employed to determine the maximum energy efficiency. Comprehensive numerical results illustrate that the proposed scheme attains higher worst-case energy efficiency as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme. PMID:28927019

Use of Convexity in Ostomy Care: Results of an International Consensus Meeting.

PubMed

Hoeflok, Jo; Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel

Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coffrin, Carleton James; Hijazi, Hassan L; Van Hentenryck, Pascal R

Here this work revisits the Semidefine Programming (SDP) relaxation of the AC power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the Convex Quadratic (QC) relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% ofmore » the open cases considered, leaving only 8 for future investigation.« less

Automated bone segmentation from dental CBCT images using patch-based sparse representation and convex optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Li; Gao, Yaozong; Shi, Feng

Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segmentmore » CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT segmentation based on 15 patients.« less

Detection of Convexity and Concavity in Context

ERIC Educational Resources Information Center

Bertamini, Marco

2008-01-01

Sensitivity to shape changes was measured, in particular detection of convexity and concavity changes. The available data are contradictory. The author used a change detection task and simple polygons to systematically manipulate convexity/concavity. Performance was high for detecting a change of sign (a new concave vertex along a convex contour…

Posterior multilevel vertebral osteotomy for correction of severe and rigid neuromuscular scoliosis: a preliminary study.

PubMed

Suh, Seung Woo; Modi, Hitesh N; Yang, Jaehyuk; Song, Hae-Ryong; Jang, Ki-Mo

2009-05-20

Prospective study. To determine the effectiveness and correction with posterior multilevel vertebral osteotomy in severe and rigid curves without anterior release. For the correction of severe and rigid scoliotic curve, anterior-posterior combined or posterior vertebral column resection (PVCR) procedures are used. Anterior procedure might compromise pulmonary functions, and PVCR might carry risk of neurologic injuries. Therefore, authors developed a new technique, which reduces both. Thirteen neuromuscular patients (7 cerebral palsy, 2 Duchenne muscular dystrophy, and 4 spinal muscular atrophy) who had rigid curve >100 degrees were prospectively selected. All were operated with posterior-only approach using pedicle screw construct. To achieve desired correction, posterior multilevel vertebral osteotomies were performed at 3 to 5 levels (apex, and 1-2 levels above and below apex) through partial laminotomy sites connecting from concave to convex side, just above the pedicle; and repeated cantilever manipulation was applied over temporary short-segment fixation, above and below the apex, on convex side. On concave side, rod was assembled with screws and rod-derotation maneuver was performed. Finally, short-segment fixation on convex side was replaced with full-length construct. Intraoperative MEP monitoring was applied in all. Mean age was 21 years and average follow-up was 25 months. Average preoperative flexibility was 20.3% (24.1 degrees). Average Cobb's angle, pelvic obliquity, and apical rotation were 118.2 degrees, 16.7 degrees, and 57 degrees preoperatively, respectively, and 48.8 degrees, 8 degrees, and 43 degrees after surgery showing significant correction of 59.4%, 46.1%, and 24.5%. Average number of osteotomy level was 4.2 and average blood loss was 3356 +/- 884 mL. Mean operation time was 330 +/- 46 minutes. None of the patient required postoperative ventilator support or displayed any signs of neurologic or vascular injuries during or after the operation. This technique should be recommended because (1) it provides release of anterior column without anterior approach and (2) our results supports its superiority as a technique.

Airfoil

DOEpatents

Ristau, Neil; Siden, Gunnar Leif

2015-07-21

An airfoil includes a leading edge, a trailing edge downstream from the leading edge, a pressure surface between the leading and trailing edges, and a suction surface between the leading and trailing edges and opposite the pressure surface. A first convex section on the suction surface decreases in curvature downstream from the leading edge, and a throat on the suction surface is downstream from the first convex section. A second convex section is on the suction surface downstream from the throat, and a first convex segment of the second convex section increases in curvature.

Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

NASA Astrophysics Data System (ADS)

Bendory, Tamir; Eldar, Yonina C.

2015-12-01

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

Portfolios with nonlinear constraints and spin glasses

NASA Astrophysics Data System (ADS)

Gábor, Adrienn; Kondor, I.

1999-12-01

In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

Emergence of Fundamental Limits in Spatially Distributed Dynamical Networks and Their Tradeoffs

DTIC Science & Technology

2017-05-01

It is shown that the resulting non -convex optimization problem can be equivalently reformulated into a rank-constrained problem. We then...display a current ly valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM- YYYY) ,2. REPORT TYPE 3...robustness in distributed control and dynamical systems. Our research re- sults are highly relevant for analysis and synthesis of engineered and natural

Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods

DTIC Science & Technology

2016-11-16

determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a suitable...pro- ceeds from the determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a...design of statistical estimators (i.e. sensors) as their respective inverses act as lower bounds to the (co)variances of the subject estimator, a property

Superiorization with level control

NASA Astrophysics Data System (ADS)

Cegielski, Andrzej; Al-Musallam, Fadhel

2017-04-01

The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com; Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr; Çelik, Nuri, E-mail: ncelik@bartin.edu.tr

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy treatment

NASA Astrophysics Data System (ADS)

Bonacker, Esther; Gibali, Aviv; Küfer, Karl-Heinz; Süss, Philipp

2017-04-01

Multicriteria optimization problems occur in many real life applications, for example in cancer radiotherapy treatment and in particular in intensity modulated radiation therapy (IMRT). In this work we focus on optimization problems with multiple objectives that are ranked according to their importance. We solve these problems numerically by combining lexicographic optimization with our recently proposed level set scheme, which yields a sequence of auxiliary convex feasibility problems; solved here via projection methods. The projection enables us to combine the newly introduced superiorization methodology with multicriteria optimization methods to speed up computation while guaranteeing convergence of the optimization. We demonstrate our scheme with a simple 2D academic example (used in the literature) and also present results from calculations on four real head neck cases in IMRT (Radiation Oncology of the Ludwig-Maximilians University, Munich, Germany) for two different choices of superiorization parameter sets suited to yield fast convergence for each case individually or robust behavior for all four cases.

Spectrum synthesis for a spectrally tunable light source based on a DMD-convex grating Offner configuration

NASA Astrophysics Data System (ADS)

Ma, Suodong; Pan, Qiao; Shen, Weimin

2016-09-01

As one kind of light source simulation devices, spectrally tunable light sources are able to generate specific spectral shape and radiant intensity outputs according to different application requirements, which have urgent demands in many fields of the national economy and the national defense industry. Compared with the LED-type spectrally tunable light source, the one based on a DMD-convex grating Offner configuration has advantages of high spectral resolution, strong digital controllability, high spectrum synthesis accuracy, etc. As a key link of the above type light source to achieve target spectrum outputs, spectrum synthesis algorithm based on spectrum matching is therefore very important. An improved spectrum synthesis algorithm based on linear least square initialization and Levenberg-Marquardt iterative optimization is proposed in this paper on the basis of in-depth study of the spectrum matching principle. The effectiveness of the proposed method is verified by a series of simulations and experimental works.

A shifted hyperbolic augmented Lagrangian-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization

NASA Astrophysics Data System (ADS)

Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite M. G. P.

2016-12-01

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. Numerical experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangian compares favorably with other deterministic and stochastic penalty-based methods.

On meeting capital requirements with a chance-constrained optimization model.

PubMed

Atta Mills, Ebenezer Fiifi Emire; Yu, Bo; Gu, Lanlan

2016-01-01

This paper deals with a capital to risk asset ratio chance-constrained optimization model in the presence of loans, treasury bill, fixed assets and non-interest earning assets. To model the dynamics of loans, we introduce a modified CreditMetrics approach. This leads to development of a deterministic convex counterpart of capital to risk asset ratio chance constraint. We pursue the scope of analyzing our model under the worst-case scenario i.e. loan default. The theoretical model is analyzed by applying numerical procedures, in order to administer valuable insights from a financial outlook. Our results suggest that, our capital to risk asset ratio chance-constrained optimization model guarantees banks of meeting capital requirements of Basel III with a likelihood of 95 % irrespective of changes in future market value of assets.

An Application of Variational Theory to an Integrated Walrasian Model of Exchange, Consumption and Production

NASA Astrophysics Data System (ADS)

Donato, M. B.; Milasi, M.; Vitanza, C.

2010-09-01

An existence result of a Walrasian equilibrium for an integrated model of exchange, consumption and production is obtained. The equilibrium model is characterized in terms of a suitable generalized quasi-variational inequality; so the existence result comes from an original technique which takes into account tools of convex and set-valued analysis.

Differentially Private Empirical Risk Minimization

PubMed Central

Chaudhuri, Kamalika; Monteleoni, Claire; Sarwate, Anand D.

2011-01-01

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the ε-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance. PMID:21892342

Diffractive optical elements on non-flat substrates using electron beam lithography

NASA Technical Reports Server (NTRS)

Maker, Paul D. (Inventor); Muller, Richard E. (Inventor); Wilson, Daniel W. (Inventor)

2002-01-01

The present disclosure describes a technique for creating diffraction gratings on curved surfaces with electron beam lithography. The curved surface can act as an optical element to produce flat and aberration-free images in imaging spectrometers. In addition, the fabrication technique can modify the power structure of the grating orders so that there is more energy in the first order than for a typical grating. The inventors noticed that by using electron-beam lithography techniques, a variety of convex gratings that are well-suited to the requirements of imaging spectrometers can be manufactured.

Decomposition method for zonal resource allocation problems in telecommunication networks

NASA Astrophysics Data System (ADS)

Konnov, I. V.; Kashuba, A. Yu

2016-11-01

We consider problems of optimal resource allocation in telecommunication networks. We first give an optimization formulation for the case where the network manager aims to distribute some homogeneous resource (bandwidth) among users of one region with quadratic charge and fee functions and present simple and efficient solution methods. Next, we consider a more general problem for a provider of a wireless communication network divided into zones (clusters) with common capacity constraints. We obtain a convex quadratic optimization problem involving capacity and balance constraints. By using the dual Lagrangian method with respect to the capacity constraint, we suggest to reduce the initial problem to a single-dimensional optimization problem, but calculation of the cost function value leads to independent solution of zonal problems, which coincide with the above single region problem. Some results of computational experiments confirm the applicability of the new methods.

Dynamic ADMM for Real-Time Optimal Power Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers distribution networks featuring distributed energy resources (DERs), and develops a dynamic optimization method to maximize given operational objectives in real time while adhering to relevant network constraints. The design of the dynamic algorithm is based on suitable linearization of the AC power flow equations, and it leverages the so-called alternating direction method of multipliers (ADMM). The steps of the ADMM, however, are suitably modified to accommodate appropriate measurements from the distribution network and the DERs. With the aid of these measurements, the resultant algorithm can enforce given operational constraints in spite of inaccuracies in the representation ofmore » the AC power flows, and it avoids ubiquitous metering to gather the state of noncontrollable resources. Optimality and convergence of the proposed algorithm are established in terms of tracking of the solution of a convex surrogate of the AC optimal power flow problem.« less

Dynamic ADMM for Real-Time Optimal Power Flow: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers distribution networks featuring distributed energy resources (DERs), and develops a dynamic optimization method to maximize given operational objectives in real time while adhering to relevant network constraints. The design of the dynamic algorithm is based on suitable linearizations of the AC power flow equations, and it leverages the so-called alternating direction method of multipliers (ADMM). The steps of the ADMM, however, are suitably modified to accommodate appropriate measurements from the distribution network and the DERs. With the aid of these measurements, the resultant algorithm can enforce given operational constraints in spite of inaccuracies in the representation ofmore » the AC power flows, and it avoids ubiquitous metering to gather the state of non-controllable resources. Optimality and convergence of the propose algorithm are established in terms of tracking of the solution of a convex surrogate of the AC optimal power flow problem.« less

Optimal Resource Allocation for NOMA-TDMA Scheme with α-Fairness in Industrial Internet of Things.

PubMed

Sun, Yanjing; Guo, Yiyu; Li, Song; Wu, Dapeng; Wang, Bin

2018-05-15

In this paper, a joint non-orthogonal multiple access and time division multiple access (NOMA-TDMA) scheme is proposed in Industrial Internet of Things (IIoT), which allowed multiple sensors to transmit in the same time-frequency resource block using NOMA. The user scheduling, time slot allocation, and power control are jointly optimized in order to maximize the system α -fair utility under transmit power constraint and minimum rate constraint. The optimization problem is nonconvex because of the fractional objective function and the nonconvex constraints. To deal with the original problem, we firstly convert the objective function in the optimization problem into a difference of two convex functions (D.C.) form, and then propose a NOMA-TDMA-DC algorithm to exploit the global optimum. Numerical results show that the NOMA-TDMA scheme significantly outperforms the traditional orthogonal multiple access scheme in terms of both spectral efficiency and user fairness.

A trust region-based approach to optimize triple response systems

NASA Astrophysics Data System (ADS)

Fan, Shu-Kai S.; Fan, Chihhao; Huang, Chia-Fen

2014-05-01

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke-Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.

The role of convexity in perception of symmetry and in visual short-term memory.

PubMed

Bertamini, Marco; Helmy, Mai Salah; Hulleman, Johan

2013-01-01

Visual perception of shape is affected by coding of local convexities and concavities. For instance, a recent study reported that deviations from symmetry carried by convexities were easier to detect than deviations carried by concavities. We removed some confounds and extended this work from a detection of reflection of a contour (i.e., bilateral symmetry), to a detection of repetition of a contour (i.e., translational symmetry). We tested whether any convexity advantage is specific to bilateral symmetry in a two-interval (Experiment 1) and a single-interval (Experiment 2) detection task. In both, we found a convexity advantage only for repetition. When we removed the need to choose which region of the contour to monitor (Experiment 3) the effect disappeared. In a second series of studies, we again used shapes with multiple convex or concave features. Participants performed a change detection task in which only one of the features could change. We did not find any evidence that convexities are special in visual short-term memory, when the to-be-remembered features only changed shape (Experiment 4), when they changed shape and changed from concave to convex and vice versa (Experiment 5), or when these conditions were mixed (Experiment 6). We did find a small advantage for coding convexity as well as concavity over an isolated (and thus ambiguous) contour. The latter is consistent with the known effect of closure on processing of shape. We conclude that convexity plays a role in many perceptual tasks but that it does not have a basic encoding advantage over concavity.

A Survey of Mathematical Programming in the Soviet Union (Bibliography),

DTIC Science & Technology

1982-01-01

ASTAFYEV, N. N., "METHOD OF LINEARIZATION IN CONVEX PROGRAMMING", TR4- Y ZIMN SHKOLY PO MAT PROGRAMMIR I XMEZHN VOPR DROGOBYCH, 72, VOL. 3, 54-73 2...AKADEMIYA KOMMUNLN’NOGO KHOZYAYSTVA (MOSCOW), 72, NO. 93, 70-77 19. GIMELFARB , G, V. MARCHENKO, V. RYBAK, "AUTOMATIC IDENTIFICATION OF IDENTICAL POINTS...DYNAMIC PROGRAMMING (CONTINUED) 25. KOLOSOV, G. Y , "ON ANALYTICAL SOLUTION OF DESIGN PROBLEMS FOR DISTRIBUTED OPTIMAL CONTROL SYSTEMS SUBJECTED TO RANDOM

Design and simulation of MEMS-actuated adjustable optical wedge for laser beam scanners

NASA Astrophysics Data System (ADS)

Bahgat, Ahmed S.; Zaki, Ahmed H.; Abdo Mohamed, Mohamed; El Sherif, Ashraf Fathy

2018-01-01

This paper introduces both optical and mechanical design and simulation of large static deflection MOEMS actuator. The designed device is in the form of an adjustable optical wedge (AOW) laser scanner. The AOW is formed of 1.5-mm-diameter plano-convex lens separated by air gap from plano-concave fixed lens. The convex lens is actuated by staggered vertical comb drive and suspended by rectangular cross-section torsion beam. An optical analysis and simulation of air separated AOW as well as detailed design, analysis, and static simulation of comb -drive are introduced. The dynamic step response of the full system is also introduced. The analytical solution showed a good agreement with the simulation results. A general global minimum optimization algorithm is applied to the comb-drive design to minimize driving voltage. A maximum comb-drive mechanical deflection angle of 12 deg in each direction was obtained under DC actuation voltage of 32 V with a settling time of 90 ms, leading to 1-mm one-dimensional (1-D) steering of laser beam with continuous optical scan angle of 5 deg in each direction. This optimization process provided a design of larger deflection actuator with smaller driving voltage compared with other conventional devices. This enhancement could lead to better performance of MOEMS-based laser beam scanners for imaging and low-speed applications.

The perception of minimal structures: performance on open and closed versions of visually presented Euclidean travelling salesperson problems.

PubMed

Vickers, Douglas; Bovet, Pierre; Lee, Michael D; Hughes, Peter

2003-01-01

The planar Euclidean version of the travelling salesperson problem (TSP) requires finding a tour of minimal length through a two-dimensional set of nodes. Despite the computational intractability of the TSP, people can produce rapid, near-optimal solutions to visually presented versions of such problems. To explain this, MacGregor et al (1999, Perception 28 1417-1428) have suggested that people use a global-to-local process, based on a perceptual tendency to organise stimuli into convex figures. We review the evidence for this idea and propose an alternative, local-to-global hypothesis, based on the detection of least distances between the nodes in an array. We present the results of an experiment in which we examined the relationships between three objective measures and performance measures of optimality and response uncertainty in tasks requiring participants to construct a closed tour or an open path. The data are not well accounted for by a process based on the convex hull. In contrast, results are generally consistent with a locally focused process based initially on the detection of nearest-neighbour clusters. Individual differences are interpreted in terms of a hierarchical process of constructing solutions, and the findings are related to a more general analysis of the role of nearest neighbours in the perception of structure and motion.

Generalized Bregman distances and convergence rates for non-convex regularization methods

NASA Astrophysics Data System (ADS)

Grasmair, Markus

2010-11-01

We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ1/p holds, if the regularization term has a slightly faster growth at zero than |t|p.

Active Mirror Predictive and Requirements Verification Software (AMP-ReVS)

NASA Technical Reports Server (NTRS)

Basinger, Scott A.

2012-01-01

This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the software package can be used to verify that the underlying requirements have been met.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, L; Han, Y; Jin, M

Purpose: To develop an iterative reconstruction method for X-ray CT, in which the reconstruction can quickly converge to the desired solution with much reduced projection views. Methods: The reconstruction is formulated as a convex feasibility problem, i.e. the solution is an intersection of three convex sets: 1) data fidelity (DF) set – the L2 norm of the difference of observed projections and those from the reconstructed image is no greater than an error bound; 2) non-negativity of image voxels (NN) set; and 3) piecewise constant (PC) set - the total variation (TV) of the reconstructed image is no greater thanmore » an upper bound. The solution can be found by applying projection onto convex sets (POCS) sequentially for these three convex sets. Specifically, the algebraic reconstruction technique and setting negative voxels as zero are used for projection onto the DF and NN sets, respectively, while the projection onto the PC set is achieved by solving a standard Rudin, Osher, and Fatemi (ROF) model. The proposed method is named as full sequential POCS (FS-POCS), which is tested using the Shepp-Logan phantom and the Catphan600 phantom and compared with two similar algorithms, TV-POCS and CP-TV. Results: Using the Shepp-Logan phantom, the root mean square error (RMSE) of reconstructed images changing along with the number of iterations is used as the convergence measurement. In general, FS- POCS converges faster than TV-POCS and CP-TV, especially with fewer projection views. FS-POCS can also achieve accurate reconstruction of cone-beam CT of the Catphan600 phantom using only 54 views, comparable to that of FDK using 364 views. Conclusion: We developed an efficient iterative reconstruction for sparse-view CT using full sequential POCS. The simulation and physical phantom data demonstrated the computational efficiency and effectiveness of FS-POCS.« less

First Evaluation of the New Thin Convex Probe Endobronchial Ultrasound Scope: A Human Ex Vivo Lung Study.

PubMed

Patel, Priya; Wada, Hironobu; Hu, Hsin-Pei; Hirohashi, Kentaro; Kato, Tatsuya; Ujiie, Hideki; Ahn, Jin Young; Lee, Daiyoon; Geddie, William; Yasufuku, Kazuhiro

2017-04-01

Endobronchial ultrasonography (EBUS)-guided transbronchial needle aspiration allows for sampling of mediastinal lymph nodes. The external diameter, rigidity, and angulation of the convex probe EBUS renders limited accessibility. This study compares the accessibility and transbronchial needle aspiration capability of the prototype thin convex probe EBUS against the convex probe EBUS in human ex vivo lungs rejected for transplant. The prototype thin convex probe EBUS (BF-Y0055; Olympus, Tokyo, Japan) with a thinner tip (5.9 mm), greater upward angle (170 degrees), and decreased forward oblique direction of view (20 degrees) was compared with the current convex probe EBUS (6.9-mm tip, 120 degrees, and 35 degrees, respectively). Accessibility and transbronchial needle aspiration capability was assessed in ex vivo human lungs declined for lung transplant. The distance of maximum reach and sustainable endoscopic limit were measured. Transbronchial needle aspiration capability was assessed using the prototype 25G aspiration needle in segmental lymph nodes. In all evaluated lungs (n = 5), the thin convex probe EBUS demonstrated greater reach and a higher success rate, averaging 22.1 mm greater maximum reach and 10.3 mm further endoscopic visibility range than convex probe EBUS, and could assess selectively almost all segmental bronchi (98% right, 91% left), demonstrating nearly twice the accessibility as the convex probe EBUS (48% right, 47% left). The prototype successfully enabled cytologic assessment of subsegmental lymph nodes with adequate quality using the dedicated 25G aspiration needle. Thin convex probe EBUS has greater accessibility to peripheral airways in human lungs and is capable of sampling segmental lymph nodes using the aspiration needle. That will allow for more precise assessment of N1 nodes and, possibly, intrapulmonary lesions normally inaccessible to the conventional convex probe EBUS. Copyright © 2017 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

A Modified Artificial Bee Colony Algorithm Application for Economic Environmental Dispatch

NASA Astrophysics Data System (ADS)

Tarafdar Hagh, M.; Baghban Orandi, Omid

2018-03-01

In conventional fossil-fuel power systems, the economic environmental dispatch (EED) problem is a major problem that optimally determines the output power of generating units in a way that cost of total production and emission level be minimized simultaneously, and at the same time all the constraints of units and system are satisfied properly. To solve EED problem which is a non-convex optimization problem, a modified artificial bee colony (MABC) algorithm is proposed in this paper. This algorithm by implementing weighted sum method is applied on two test systems, and eventually, obtained results are compared with other reported results. Comparison of results confirms superiority and efficiency of proposed method clearly.

On the convergence of a linesearch based proximal-gradient method for nonconvex optimization

NASA Astrophysics Data System (ADS)

Bonettini, S.; Loris, I.; Porta, F.; Prato, M.; Rebegoldi, S.

2017-05-01

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Łojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications.

ANOTHER LOOK AT THE FAST ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM (FISTA)*

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2017-01-01

This paper provides a new way of developing the “Fast Iterative Shrinkage/Thresholding Algorithm (FISTA)” [3] that is widely used for minimizing composite convex functions with a nonsmooth term such as the ℓ1 regularizer. In particular, this paper shows that FISTA corresponds to an optimized approach to accelerating the proximal gradient method with respect to a worst-case bound of the cost function. This paper then proposes a new algorithm that is derived by instead optimizing the step coefficients of the proximal gradient method with respect to a worst-case bound of the composite gradient mapping. The proof is based on the worst-case analysis called Performance Estimation Problem in [11]. PMID:29805242

Combining feature extraction and classification for fNIRS BCIs by regularized least squares optimization.

PubMed

Heger, Dominic; Herff, Christian; Schultz, Tanja

2014-01-01

In this paper, we show that multiple operations of the typical pattern recognition chain of an fNIRS-based BCI, including feature extraction and classification, can be unified by solving a convex optimization problem. We formulate a regularized least squares problem that learns a single affine transformation of raw HbO(2) and HbR signals. We show that this transformation can achieve competitive results in an fNIRS BCI classification task, as it significantly improves recognition of different levels of workload over previously published results on a publicly available n-back data set. Furthermore, we visualize the learned models and analyze their spatio-temporal characteristics.

Convex composite wavelet frame and total variation-based image deblurring using nonconvex penalty functions

NASA Astrophysics Data System (ADS)

Shen, Zhengwei; Cheng, Lishuang

2017-09-01

Total variation (TV)-based image deblurring method can bring on staircase artifacts in the homogenous region of the latent images recovered from the degraded images while a wavelet/frame-based image deblurring method will lead to spurious noise spikes and pseudo-Gibbs artifacts in the vicinity of discontinuities of the latent images. To suppress these artifacts efficiently, we propose a nonconvex composite wavelet/frame and TV-based image deblurring model. In this model, the wavelet/frame and the TV-based methods may complement each other, which are verified by theoretical analysis and experimental results. To further improve the quality of the latent images, nonconvex penalty function is used to be the regularization terms of the model, which may induce a stronger sparse solution and will more accurately estimate the relative large gradient or wavelet/frame coefficients of the latent images. In addition, by choosing a suitable parameter to the nonconvex penalty function, the subproblem that splits by the alternative direction method of multipliers algorithm from the proposed model can be guaranteed to be a convex optimization problem; hence, each subproblem can converge to a global optimum. The mean doubly augmented Lagrangian and the isotropic split Bregman algorithms are used to solve these convex subproblems where the designed proximal operator is used to reduce the computational complexity of the algorithms. Extensive numerical experiments indicate that the proposed model and algorithms are comparable to other state-of-the-art model and methods.

An objective function exploiting suboptimal solutions in metabolic networks

PubMed Central

2013-01-01

Background Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power. Results We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation. Conclusion Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network. PMID:24088221

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

PubMed

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

PubMed Central

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-01-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques. PMID:21552465

Noncontact methods for optical testing of convex aspheric mirrors for future large telescopes

NASA Astrophysics Data System (ADS)

Goncharov, Alexander V.; Druzhin, Vladislav V.; Batshev, Vladislav I.

2009-06-01

Non-contact methods for testing of large rotationally symmetric convex aspheric mirrors are proposed. These methods are based on non-null testing with side illumination schemes, in which a narrow collimated beam is reflected from the meridional aspheric profile of a mirror. The figure error of the mirror is deduced from the intensity pattern from the reflected beam obtained on a screen, which is positioned in the tangential plane (containing the optical axis) and perpendicular to the incoming beam. Testing of the entire surface is carried out by rotating the mirror about its optical axis and registering the characteristics of the intensity pattern on the screen. The intensity pattern can be formed using three different techniques: modified Hartman test, interference and boundary curve test. All these techniques are well known but have not been used in the proposed side illumination scheme. Analytical expressions characterizing the shape and location of the intensity pattern on the screen or a CCD have been developed for all types of conic surfaces. The main advantage of these testing methods compared with existing methods (Hindle sphere, null lens, computer generated hologram) is that the reference system does not require large optical components.

Radius of convexity of a certain class of close-to-convex functions

NASA Astrophysics Data System (ADS)

Yahya, Abdullah; Soh, Shaharuddin Cik

2017-11-01

In the present paper, we consider and investigate a certain class of close-to-convex functions that defined in the unit disk, U = {z : |z| < 1}, which denotes as Re { ei αz/f '(z ) f (z )-f (-z ) } >δ where |α| < π, cos (α) > δ and 0 δ <1. Furthermore, we obtain preliminary result for bound f'(z) and determine result for radius of convexity.

Convex Graph Invariants

DTIC Science & Technology

2010-12-02

Motzkin, T. and Straus, E. (1965). Maxima for graphs and a new proof of a theorem of Turan . Canad. J. Math. 17 533–540. [33] Rendl, F. and Sotirov, R...Convex Graph Invariants Venkat Chandrasekaran, Pablo A . Parrilo, and Alan S. Willsky ∗ Laboratory for Information and Decision Systems Department of...this paper we study convex graph invariants, which are graph invariants that are convex functions of the adjacency matrix of a graph. Some examples

Allometric relationships between traveltime channel networks, convex hulls, and convexity measures

NASA Astrophysics Data System (ADS)

Tay, Lea Tien; Sagar, B. S. Daya; Chuah, Hean Teik

2006-06-01

The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and areas of corresponding convex hulls C(Sn), the ratios of which provide convexity measures CM(Sn) of traveltime networks. A statistically significant scaling relationship is found for a model network in the form L(Sn) ˜ A[C(Sn)]0.57. From the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures, new power law relations are derived. Such relations for a model network are CM(Sn) ˜ ? and CM(Sn) ˜ ?. In addition to the model study, these relations for networks derived from seven subbasins of Cameron Highlands region of Peninsular Malaysia are provided. Further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks.

Time-frequency filtering and synthesis from convex projections

NASA Astrophysics Data System (ADS)

White, Langford B.

1990-11-01

This paper describes the application of the theory of projections onto convex sets to time-frequency filtering and synthesis problems. We show that the class of Wigner-Ville Distributions (WVD) of L2 signals form the boundary of a closed convex subset of L2(R2). This result is obtained by considering the convex set of states on the Heisenberg group of which the ambiguity functions form the extreme points. The form of the projection onto the set of WVDs is deduced. Various linear and non-linear filtering operations are incorporated by formulation as convex projections. An example algorithm for simultaneous time-frequency filtering and synthesis is suggested.

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay.

PubMed

Sowmiya, C; Raja, R; Cao, Jinde; Rajchakit, G; Alsaedi, Ahmed

2017-01-01

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

NASA Astrophysics Data System (ADS)

Sembiring, Pasukat

2017-12-01

Processing ofdata with very large dimensions has been a hot topic in recent decades. Various techniques have been proposed in order to execute the desired information or structure. Non- Negative Matrix Factorization (NMF) based on non-negatives data has become one of the popular methods for shrinking dimensions. The main strength of this method is non-negative object, the object model by a combination of some basic non-negative parts, so as to provide a physical interpretation of the object construction. The NMF is a dimension reduction method thathasbeen used widely for numerous applications including computer vision,text mining, pattern recognitions,and bioinformatics. Mathematical formulation for NMF did not appear as a convex optimization problem and various types of algorithms have been proposed to solve the problem. The Framework of Alternative Nonnegative Least Square(ANLS) are the coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This paper proposes a new algorithm to solve NMF problem based on the framework of ANLS.This algorithm inherits the convergenceproperty of the ANLS framework to nonlinear constraints NMF formulations.

Spatial partitioning algorithms for data visualization

NASA Astrophysics Data System (ADS)

Devulapalli, Raghuveer; Quist, Mikael; Carlsson, John Gunnar

2013-12-01

Spatial partitions of an information space are frequently used for data visualization. Weighted Voronoi diagrams are among the most popular ways of dividing a space into partitions. However, the problem of computing such a partition efficiently can be challenging. For example, a natural objective is to select the weights so as to force each Voronoi region to take on a pre-defined area, which might represent the relevance or market share of an informational object. In this paper, we present an easy and fast algorithm to compute these weights of the Voronoi diagrams. Unlike previous approaches whose convergence properties are not well-understood, we give a formulation to the problem based on convex optimization with excellent performance guarantees in theory and practice. We also show how our technique can be used to control the shape of these partitions. More specifically we show how to convert undesirable skinny and long regions into fat regions while maintaining the areas of the partitions. As an application, we use these to visualize the amount of website traffic for the top 101 websites.

A methodology for the synthesis of robust feedback systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Milich, David Albert

1988-01-01

A new methodology is developed for the synthesis of linear, time-variant (LTI) controllers for multivariable LTI systems. The resulting closed-loop system is nominally stable and exhibits a known level of performance. In addition, robustness of the feedback system is guaranteed, i.e., stability and performance are retained in the presence of multiple unstructured uncertainty blocks located at various points in the feedback loop. The design technique is referred to as the Causality Recovery Methodology (CRM). The CRM relies on the Youla parameterization of all stabilizing compensators to ensure nominal stability of the feedback system. A frequency-domain inequality in terms of the structured singular value mu defines the robustness specification. The optimal compensator, with respect to the mu condition, is shown to be noncausal in general. The aim of the CRM is to find a stable, causal transfer function matrix that approximates the robustness characteristics of the optimal solution. The CRM, via a series of infinite-dimensional convex programs, produces a closed-loop system whose performance robustness is at least as good as that of any initial design. The algorithm is approximated by a finite dimensional process for the purposes of implementation. Two numerical examples confirm the potential viability of the CRM concept; however, the robustness improvement comes at the expense of increased computational burden and compensator complexity.

Molecular inspired models for prediction and control of directional FSO/RF wireless networks

NASA Astrophysics Data System (ADS)

Llorca, Jaime; Milner, Stuart D.; Davis, Christopher C.

2010-08-01

Directional wireless networks using FSO and RF transmissions provide wireless backbone support for mobile communications in dynamic environments. The heterogeneous and dynamic nature of such networks challenges their robustness and requires self-organization mechanisms to assure end-to-end broadband connectivity. We developed a framework based on the definition of a potential energy function to characterize robustness in communication networks and the study of first and second order variations of the potential energy to provide prediction and control strategies for network performance optimization. In this paper, we present non-convex molecular potentials such as the Morse Potential, used to describe the potential energy of bonds within molecules, for the characterization of communication links in the presence of physical constraints such as the power available at the network nodes. The inclusion of the Morse Potential translates into adaptive control strategies where forces on network nodes drive the release, retention or reconfiguration of communication links for network performance optimization. Simulation results show the effectiveness of our self-organized control mechanism, where the physical topology reorganizes to maximize the number of source to destination communicating pairs. Molecular Normal Mode Analysis (NMA) techniques for assessing network performance degradation in dynamic networks are also presented. Preliminary results show correlation between peaks in the eigenvalues of the Hessian of the network potential and network degradation.

Digital transceiver design for two-way AF-MIMO relay systems with imperfect CSI

NASA Astrophysics Data System (ADS)

Hu, Chia-Chang; Chou, Yu-Fei; Chen, Kui-He

2013-09-01

In the paper, combined optimization of the terminal precoders/equalizers and single-relay precoder is proposed for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-way single-relay system with correlated channel uncertainties. Both terminal transceivers and relay precoding matrix are designed based on the minimum mean square error (MMSE) criterion when terminals are unable to erase completely self-interference due to imperfect correlated channel state information (CSI). This robust joint optimization problem of beamforming and precoding matrices under power constraints belongs to neither concave nor convex so that a nonlinear matrix-form conjugate gradient (MCG) algorithm is applied to explore local optimal solutions. Simulation results show that the robust transceiver design is able to overcome effectively the loss of bit-error-rate (BER) due to inclusion of correlated channel uncertainties and residual self-interference.

Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Dhople, Sairaj V.; Giannakis, Georgios B.

This paper considers future distribution networks featuring inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of feedback controllers that seek real- and reactive-power inverter setpoints corresponding to AC optimal power flow (OPF) solutions. The objective is to bridge the temporal gap between long-term system optimization and real-time inverter control, and enable seamless PV-owner participation without compromising system efficiency and stability. The design of the controllers is grounded on a dual ..epsilon..-subgradient method, while semidefinite programming relaxations are advocated to bypass the non-convexity of AC OPF formulations. Global convergence of inverter output powers is analytically established for diminishing stepsize rules formore » cases where: i) computational limits dictate asynchronous updates of the controller signals, and ii) inverter reference inputs may be updated at a faster rate than the power-output settling time.« less

Determining optimal selling price and lot size with process reliability and partial backlogging considerations

NASA Astrophysics Data System (ADS)

Hsieh, Tsu-Pang; Cheng, Mei-Chuan; Dye, Chung-Yuan; Ouyang, Liang-Yuh

2011-01-01

In this article, we extend the classical economic production quantity (EPQ) model by proposing imperfect production processes and quality-dependent unit production cost. The demand rate is described by any convex decreasing function of the selling price. In addition, we allow for shortages and a time-proportional backlogging rate. For any given selling price, we first prove that the optimal production schedule not only exists but also is unique. Next, we show that the total profit per unit time is a concave function of price when the production schedule is given. We then provide a simple algorithm to find the optimal selling price and production schedule for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm and conclude this article with suggestions for possible future research.

A system of nonlinear set valued variational inclusions.

PubMed

Tang, Yong-Kun; Chang, Shih-Sen; Salahuddin, Salahuddin

2014-01-01

In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved. 49J40; 47H06.

Computational Role of Tunneling in a Programmable Quantum Annealer

NASA Technical Reports Server (NTRS)

Boixo, Sergio; Smelyanskiy, Vadim; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Amin, Mohammad; Mohseni, Masoud; Denchev, Vasil S.; Neven, Hartmut

2016-01-01

Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

Advanced method optimization for volatile aroma profiling of beer using two-dimensional gas chromatography time-of-flight mass spectrometry.

PubMed

Stefanuto, Pierre-Hugues; Perrault, Katelynn A; Dubois, Lena M; L'Homme, Benjamin; Allen, Catherine; Loughnane, Caitriona; Ochiai, Nobuo; Focant, Jean-François

2017-07-21

The complex mixture of volatile organic compounds (VOCs) present in the headspace of Trappist and craft beers was studied to illustrate the efficiency of thermal desorption (TD) comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC-TOFMS) for highlighting subtle differences between highly complex mixtures of VOCs. Headspace solid-phase microextraction (HS-SPME), multiple (and classical) stir bar sorptive extraction (mSBSE), static headspace (SHS), and dynamic headspace (DHS) were compared for the extraction of a set of 21 representative flavor compounds of beer aroma. A Box-Behnken surface response methodology experimental design optimization (DOE) was used for convex hull calculation (Delaunay's triangulation algorithms) of peak dispersion in the chromatographic space. The predicted value of 0.5 for the ratio between the convex hull and the available space was 10% higher than the experimental value, demonstrating the usefulness of the approach to improve optimization of the GC×GC separation. Chemical variations amongst aligned chromatograms were studied by means of Fisher Ratio (FR) determination and F-distribution threshold filtration at different significance levels (α=0.05 and 0.01) and based on z-score normalized area for data reduction. Statistically significant compounds were highlighted following principal component analysis (PCA) and hierarchical cluster analysis (HCA). The dendrogram structure not only provided clear visual information about similarities between products but also permitted direct identification of the chemicals and their relative weight in clustering. The effective coupling of DHS-TD-GC×GC-TOFMS with PCA and HCA was able to highlight the differences and common typical VOC patterns among 24 samples of different Trappist and selected Canadian craft beers. Copyright © 2017 Elsevier B.V. All rights reserved.

Application of identifying transmission spheres for spherical surface testing

NASA Astrophysics Data System (ADS)

Han, Christopher B.; Ye, Xin; Li, Xueyuan; Wang, Quanzhao; Tang, Shouhong; Han, Sen

2017-06-01

We developed a new application on Microsoft Foundation Classes (MFC) to identify correct transmission spheres (TS) for Spherical Surface Testing (SST). Spherical surfaces are important optical surfaces, and the wide application and high production rate of spherical surfaces necessitates an accurate and highly reliable measuring device. A Fizeau Interferometer is an appropriate tool for SST due to its subnanometer accuracy. It measures the contour of a spherical surface using a common path, which is insensitive to the surrounding circumstances. The Fizeau Interferometer transmits a wide laser beam, creating interference fringes from re-converging light from the transmission sphere and the test surface. To make a successful measurement, the application calculates and determines the appropriate transmission sphere for the test surface. There are 3 main inputs from the test surfaces that are utilized to determine the optimal sizes and F-numbers of the transmission spheres: (1) the curvatures (concave or convex), (2) the Radii of Curvature (ROC), and (3) the aperture sizes. The application will firstly calculate the F-numbers (i.e. ROC divided by aperture) of the test surface, secondly determine the correct aperture size of a convex surface, thirdly verify that the ROC of the test surface must be shorter than the reference surface's ROC of the transmission sphere, and lastly calculate the percentage of area that the test surface will be measured. However, the amount of interferometers and transmission spheres should be optimized when measuring large spherical surfaces to avoid requiring a large amount of interferometers and transmission spheres for each test surface. Current measuring practices involve tedious and potentially inaccurate calculations. This smart application eliminates human calculation errors, optimizes the selection of transmission spheres (including the least number required) and interferometer sizes, and increases efficiency.

CPU timing routines for a CONVEX C220 computer system

NASA Technical Reports Server (NTRS)

Bynum, Mary Ann

1989-01-01

The timing routines available on the CONVEX C220 computer system in the Structural Mechanics Division (SMD) at NASA Langley Research Center are examined. The function of the timing routines, the use of the timing routines in sequential, parallel, and vector code, and the interpretation of the results from the timing routines with respect to the CONVEX model of computing are described. The timing routines available on the SMD CONVEX fall into two groups. The first group includes standard timing routines generally available with UNIX 4.3 BSD operating systems, while the second group includes routines unique to the SMD CONVEX. The standard timing routines described in this report are /bin/csh time,/bin/time, etime, and ctime. The routines unique to the SMD CONVEX are getinfo, second, cputime, toc, and a parallel profiling package made up of palprof, palinit, and palsum.

IFIP Conference on System Modeling and Optimization (10th). Held at New York City, New York on 31 August-4 September 1981.

DTIC Science & Technology

1982-01-15

Systems U. HEILEVANN, Cyclical Taxonomy and Large Econometic Models D. HINRICHSEN, U. KRAUSE , Triangulation of Convex Polyhedra with an Application to...Classification of Economic Fluctua- tions, "Explorations in Economic Research", vol.2 (1975), pp. 167-2o2. -196- D. Hinrich3en and U. Krause Department...d’opti- misation de structures, Those de doctuer ingenieur, Universit6 de Paris VI, 1976. -211- - *. ____________________ -__-____- Wolfgang Nooss

Robust model predictive control for satellite formation keeping with eccentricity/inclination vector separation

NASA Astrophysics Data System (ADS)

Lim, Yeerang; Jung, Youeyun; Bang, Hyochoong

2018-05-01

This study presents model predictive formation control based on an eccentricity/inclination vector separation strategy. Alternative collision avoidance can be accomplished by using eccentricity/inclination vectors and adding a simple goal function term for optimization process. Real-time control is also achievable with model predictive controller based on convex formulation. Constraint-tightening approach is address as well improve robustness of the controller, and simulation results are presented to verify performance enhancement for the proposed approach.

A second order derivative scheme based on Bregman algorithm class

NASA Astrophysics Data System (ADS)

Campagna, Rosanna; Crisci, Serena; Cuomo, Salvatore; Galletti, Ardelio; Marcellino, Livia

2016-10-01

The algorithms based on the Bregman iterative regularization are known for efficiently solving convex constraint optimization problems. In this paper, we introduce a second order derivative scheme for the class of Bregman algorithms. Its properties of convergence and stability are investigated by means of numerical evidences. Moreover, we apply the proposed scheme to an isotropic Total Variation (TV) problem arising out of the Magnetic Resonance Image (MRI) denoising. Experimental results confirm that our algorithm has good performance in terms of denoising quality, effectiveness and robustness.

Joint segmentation of lumen and outer wall from femoral artery MR images: Towards 3D imaging measurements of peripheral arterial disease.

PubMed

Ukwatta, Eranga; Yuan, Jing; Qiu, Wu; Rajchl, Martin; Chiu, Bernard; Fenster, Aaron

2015-12-01

Three-dimensional (3D) measurements of peripheral arterial disease (PAD) plaque burden extracted from fast black-blood magnetic resonance (MR) images have shown to be more predictive of clinical outcomes than PAD stenosis measurements. To this end, accurate segmentation of the femoral artery lumen and outer wall is required for generating volumetric measurements of PAD plaque burden. Here, we propose a semi-automated algorithm to jointly segment the femoral artery lumen and outer wall surfaces from 3D black-blood MR images, which are reoriented and reconstructed along the medial axis of the femoral artery to obtain improved spatial coherence between slices of the long, thin femoral artery and to reduce computation time. The developed segmentation algorithm enforces two priors in a global optimization manner: the spatial consistency between the adjacent 2D slices and the anatomical region order between the femoral artery lumen and outer wall surfaces. The formulated combinatorial optimization problem for segmentation is solved globally and exactly by means of convex relaxation using a coupled continuous max-flow (CCMF) model, which is a dual formulation to the convex relaxed optimization problem. In addition, the CCMF model directly derives an efficient duality-based algorithm based on the modern multiplier augmented optimization scheme, which has been implemented on a GPU for fast computation. The computed segmentations from the developed algorithm were compared to manual delineations from experts using 20 black-blood MR images. The developed algorithm yielded both high accuracy (Dice similarity coefficients ≥ 87% for both the lumen and outer wall surfaces) and high reproducibility (intra-class correlation coefficient of 0.95 for generating vessel wall area), while outperforming the state-of-the-art method in terms of computational time by a factor of ≈ 20. Copyright © 2015 Elsevier B.V. All rights reserved.

Signal processing using sparse derivatives with applications to chromatograms and ECG

NASA Astrophysics Data System (ADS)

Ning, Xiaoran

In this thesis, we investigate the sparsity exist in the derivative domain. Particularly, we focus on the type of signals which posses up to Mth (M > 0) order sparse derivatives. Efforts are put on formulating proper penalty functions and optimization problems to capture properties related to sparse derivatives, searching for fast, computationally efficient solvers. Also the effectiveness of these algorithms are applied to two real world applications. In the first application, we provide an algorithm which jointly addresses the problems of chromatogram baseline correction and noise reduction. The series of chromatogram peaks are modeled as sparse with sparse derivatives, and the baseline is modeled as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is also utilized with symmetric penalty functions. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. Promising result is obtained. In the second application, a novel Electrocardiography (ECG) enhancement algorithm is designed also based on sparse derivatives. In the real medical environment, ECG signals are often contaminated by various kinds of noise or artifacts, for example, morphological changes due to motion artifact, non-stationary noise due to muscular contraction (EMG), etc. Some of these contaminations severely affect the usefulness of ECG signals, especially when computer aided algorithms are utilized. By solving the proposed convex l1 optimization problem, artifacts are reduced by modeling the clean ECG signal as a sum of two signals whose second and third-order derivatives (differences) are sparse respectively. At the end, the algorithm is applied to a QRS detection system and validated using the MIT-BIH Arrhythmia database (109452 anotations), resulting a sensitivity of Se = 99.87%$ and a positive prediction of +P = 99.88%.

Usefulness of the convexity apparent hyperperfusion sign in 123I-iodoamphetamine brain perfusion SPECT for the diagnosis of idiopathic normal pressure hydrocephalus.

PubMed

Ohmichi, Takuma; Kondo, Masaki; Itsukage, Masahiro; Koizumi, Hidetaka; Matsushima, Shigenori; Kuriyama, Nagato; Ishii, Kazunari; Mori, Etsuro; Yamada, Kei; Mizuno, Toshiki; Tokuda, Takahiko

2018-03-16

OBJECTIVE The gold standard for the diagnosis of idiopathic normal pressure hydrocephalus (iNPH) is the CSF removal test. For elderly patients, however, a less invasive diagnostic method is required. On MRI, high-convexity tightness was reported to be an important finding for the diagnosis of iNPH. On SPECT, patients with iNPH often show hyperperfusion of the high-convexity area. The authors tested 2 hypotheses regarding the SPECT finding: 1) it is relative hyperperfusion reflecting the increased gray matter density of the convexity, and 2) it is useful for the diagnosis of iNPH. The authors termed the SPECT finding the convexity apparent hyperperfusion (CAPPAH) sign. METHODS Two clinical studies were conducted. In study 1, SPECT was performed for 20 patients suspected of having iNPH, and regional cerebral blood flow (rCBF) of the high-convexity area was examined using quantitative analysis. Clinical differences between patients with the CAPPAH sign (CAP) and those without it (NCAP) were also compared. In study 2, the CAPPAH sign was retrospectively assessed in 30 patients with iNPH and 19 healthy controls using SPECT images and 3D stereotactic surface projection. RESULTS In study 1, rCBF of the high-convexity area of the CAP group was calculated as 35.2-43.7 ml/min/100 g, which is not higher than normal values of rCBF determined by SPECT. The NCAP group showed lower cognitive function and weaker responses to the removal of CSF than the CAP group. In study 2, the CAPPAH sign was positive only in patients with iNPH (24/30) and not in controls (sensitivity 80%, specificity 100%). The coincidence rate between tight high convexity on MRI and the CAPPAH sign was very high (28/30). CONCLUSIONS Patients with iNPH showed hyperperfusion of the high-convexity area on SPECT; however, the presence of the CAPPAH sign did not indicate real hyperperfusion of rCBF in the high-convexity area. The authors speculated that patients with iNPH without the CAPPAH sign, despite showing tight high convexity on MRI, might have comorbidities such as Alzheimer's disease.

Multi-objective optimal dispatch of distributed energy resources

NASA Astrophysics Data System (ADS)

Longe, Ayomide

This thesis is composed of two papers which investigate the optimal dispatch for distributed energy resources. In the first paper, an economic dispatch problem for a community microgrid is studied. In this microgrid, each agent pursues an economic dispatch for its personal resources. In addition, each agent is capable of trading electricity with other agents through a local energy market. In this paper, a simple market structure is introduced as a framework for energy trades in a small community microgrid such as the Solar Village. It was found that both sellers and buyers benefited by participating in this market. In the second paper, Semidefinite Programming (SDP) for convex relaxation of power flow equations is used for optimal active and reactive dispatch for Distributed Energy Resources (DER). Various objective functions including voltage regulation, reduced transmission line power losses, and minimized reactive power charges for a microgrid are introduced. Combinations of these goals are attained by solving a multiobjective optimization for the proposed ORPD problem. Also, both centralized and distributed versions of this optimal dispatch are investigated. It was found that SDP made the optimal dispatch faster and distributed solution allowed for scalability.

SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ungun, B; Stanford University School of Medicine, Stanford, CA; Fu, A

2016-06-15

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction,more » we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.« less

Radar/Sonar and Time Series Analysis

DTIC Science & Technology

1991-06-27

Davis, William Dunsmuir Fourier and Likelihood Analysis in NMR Spectroscopy .......... David Brillinger and Reinhold Kaiser Resampling Techniques for...Zubelli. 2:30 pm Gunter Meyer The parabolic Fock theory for a convex dielectric Georgia Tech. scatterer Abstract: This talk deals with a high frequency...Lincoln Laboratory, MIT Jun 18 - Jun 29 Gunter Meyer Georgia Institute of Technology Jun 25 - Jun 29 Willard Miller University of Minnesota Ruth Miniowitz

A Generalized Distance’ Estimation Procedure for Intra-Urban Interaction

DTIC Science & Technology

Bettinger . It is found that available estimation techniques necessarily result in non-integer solutions. A mathematical device is therefore...The estimation of urban and regional travel patterns has been a necessary part of current efforts to establish land use guidelines for the Texas...paper details computational experience with travel estimation within Corpus Christi, Texas, using a new convex programming approach of Charnes, Raike and

A 'range test' for determining scatterers with unknown physical properties

NASA Astrophysics Data System (ADS)

Potthast, Roland; Sylvester, John; Kusiak, Steven

2003-06-01

We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subset of the scatterer and provides information about its location and estimates for its shape. For convex polygonal scatterers the scattering support coincides with the scatterer and we obtain full shape reconstructions. The method will be formulated for the reconstruction of the scatterers from the far field pattern for one or a few incident waves. The method is non-iterative in nature and belongs to the type of recently derived generalized sampling schemes such as the 'no response test' of Luke-Potthast. The range test operates by testing whether it is possible to analytically continue a far field to the exterior of any test domain Omegatest. By intersecting the convex hulls of various test domains we can produce a minimal convex set, the convex scattering support of which must be contained in the convex hull of the support of any scatterer which produces that far field. The convex scattering support is calculated by testing the range of special integral operators for a sampling set of test domains. The numerical results can be used as an approximation for the support of the unknown scatterer. We prove convergence and regularity of the scheme and show numerical examples for sound-soft, sound-hard and medium scatterers. We can apply the range test to non-convex scatterers as well. We can conclude that an Omegatest which passes the range test has a non-empty intersection with the infinity-support (the complement of the unbounded component of the complement of the support) of the true scatterer, but cannot find a minimal set which must be contained therein.

Duality of caustics in Minkowski billiards

NASA Astrophysics Data System (ADS)

Artstein-Avidan, S.; Florentin, D. I.; Ostrover, Y.; Rosen, D.

2018-04-01

In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth, centrally symmetric, strictly convex body K, for every convex caustic which K possesses, the ‘dual’ billiard dynamics in which the table is the Euclidean unit ball and the geometry that governs the motion is induced by the body K, possesses a dual convex caustic. Such a pair of caustics are dual in a strong sense, and in particular they have the same perimeter, Lazutkin parameter (both measured with respect to the corresponding geometries), and rotation number. We show moreover that for general Minkowski billiards this phenomenon fails, and one can construct a smooth caustic in a Minkowski billiard table which possesses no dual convex caustic.

Effective light absorption and its enhancement factor for silicon nanowire-based solar cell.

PubMed

Duan, Zhiqiang; Li, Meicheng; Mwenya, Trevor; Fu, Pengfei; Li, Yingfeng; Song, Dandan

2016-01-01

Although nanowire (NW) antireflection coating can enhance light trapping capability, which is generally used in crystal silicon (CS) based solar cells, whether it can improve light absorption in the CS body depends on the NW geometrical shape and their geometrical parameters. In order to conveniently compare with the bare silicon, two enhancement factors E(T) and E(A) are defined and introduced to quantitatively evaluate the efficient light trapping capability of NW antireflective layer and the effective light absorption capability of CS body. Five different shapes (cylindrical, truncated conical, convex conical, conical, and concave conical) of silicon NW arrays arranged in a square are studied, and the theoretical results indicate that excellent light trapping does not mean more light can be absorbed in the CS body. The convex conical NW has the best light trapping, but the concave conical NW has the best effective light absorption. Furthermore, if the cross section of silicon NW is changed into a square, both light trapping and effective light absorption are enhanced, and the Eiffel Tower shaped NW arrays have optimal effective light absorption.

Fabrication and evaluation of variable focus and large deformation plano-convex microlens based on non-ionic poly(vinyl chloride)/dibutyl adipate gels

NASA Astrophysics Data System (ADS)

Kim, Sang-Youn; Yeo, Myoung; Shin, Eun-Jae; Park, Won-Hyeong; Jang, Jong-Seok; Nam, Byeong-Uk; Bae, Jin Woo

2015-11-01

In this paper, we propose a variable focus microlens module based on a transparent, electroactive, and non-ionic PVC/DBA gel. A non-ionic PVC/DBA (nPVC) gel on an ITO glass was confined beneath a rigid annular electrode, and applied pressure squeezed a bulge of the nPVC gel into the annular electrode, resulting in a hemispherical plano-convex nPVC gel microlens. The proposed nPVC gel microlens was analyzed and optimized. When voltage is applied to the circular perimeter (the annular electrode) of this fabricated microlens, electrically induced creep deformation of the nPVC gel occurs, changing its optical focal length. The focal length remarkably increases from 3.8 mm up to 14.3 mm with increasing applied voltages from 300 V to 800 V. Due to its compact, transparent, and electroactive characteristics, the proposed nPVC gel microlens can be easily inserted into small consumer electronic devices, such as digital cameras, camcorders, cell phones, and other portable optical devices.

Exploring metabolic pathways in genome-scale networks via generating flux modes.

PubMed

Rezola, A; de Figueiredo, L F; Brock, M; Pey, J; Podhorski, A; Wittmann, C; Schuster, S; Bockmayr, A; Planes, F J

2011-02-15

The reconstruction of metabolic networks at the genome scale has allowed the analysis of metabolic pathways at an unprecedented level of complexity. Elementary flux modes (EFMs) are an appropriate concept for such analysis. However, their number grows in a combinatorial fashion as the size of the metabolic network increases, which renders the application of EFMs approach to large metabolic networks difficult. Novel methods are expected to deal with such complexity. In this article, we present a novel optimization-based method for determining a minimal generating set of EFMs, i.e. a convex basis. We show that a subset of elements of this convex basis can be effectively computed even in large metabolic networks. Our method was applied to examine the structure of pathways producing lysine in Escherichia coli. We obtained a more varied and informative set of pathways in comparison with existing methods. In addition, an alternative pathway to produce lysine was identified using a detour via propionyl-CoA, which shows the predictive power of our novel approach. The source code in C++ is available upon request.

On approximation and energy estimates for delta 6-convex functions.

PubMed

Saleem, Muhammad Shoaib; Pečarić, Josip; Rehman, Nasir; Khan, Muhammad Wahab; Zahoor, Muhammad Sajid

2018-01-01

The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.

Assessing the influence of lower facial profile convexity on perceived attractiveness in the orthognathic patient, clinician, and layperson.

PubMed

Naini, Farhad B; Donaldson, Ana Nora A; McDonald, Fraser; Cobourne, Martyn T

2012-09-01

The aim was a quantitative evaluation of how the severity of lower facial profile convexity influences perceived attractiveness. The lower facial profile of an idealized image was altered incrementally between 14° to -16°. Images were rated on a Likert scale by orthognathic patients, laypeople, and clinicians. Attractiveness ratings were greater for straight profiles in relation to convex/concave, with no significant difference between convex and concave profiles. Ratings decreased by 0.23 of a level for every degree increase in the convexity angle. Class II/III patients gave significantly reduced ratings of attractiveness and had greater desire for surgery than class I. A straight profile is perceived as most attractive and greater degrees of convexity or concavity deemed progressively less attractive, but a range of 10° to -12° may be deemed acceptable; beyond these values surgical correction is desired. Patients are most critical, and clinicians are more critical than laypeople. Copyright © 2012 Elsevier Inc. All rights reserved.

The spectral positioning algorithm of new spectrum vehicle based on convex programming in wireless sensor network

NASA Astrophysics Data System (ADS)

Zhang, Yongjun; Lu, Zhixin

2017-10-01

Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.

A path to asteroid bulk densities: Simultaneous size and shape optimization from optical lightcurves and Keck disk-resolved data

NASA Astrophysics Data System (ADS)

Hanus, Josef; Viikinkoski, Matti; Marchis, Franck; Durech, Josef

2015-11-01

A reliable bulk density of an asteroid can be determined from the knowledge of its volume and mass. This quantity provides hints on the internal structure of asteroids and their origin. We compute volume of several asteroids by scaling sizes of their 3D shape models to fit the disk-resolved images, which are available in the Keck Observatory Archive (KOA) and the Virtual Observatory Binary Asteroids Database (VOBAD). The size of an asteroid is optimized together with its shape by the All-Data Asteroid Modelling inversion algorithm (ADAM, Viikinkoski et al., 2015, A&A, 576, A8), while the spin state of the original convex shape model from the DAMIT database is only used as an initial guess for the modeling. Updated sets of optical lightcurves are usually employed. Thereafter, we combine obtained volume with mass estimates available in the literature and derive bulk densities for tens of asteroids with a typical accuracy of 20-50%.On top of that, we also provide a list of asteroids, for which (i) there are already mass estimates with reported uncertainties better than 20% or their masses will be most likely determined in the future from Gaia astrometric observations, and (ii) their 3D shape models are currently unknown. Additional optical lightcurves are necessary in order to determine convex shape models of these asteroids. Our web page (https://asteroid-obs.oca.eu/foswiki/bin/view/Main/Photometry) contains additional information about this observation campaign.

A convex optimization approach for identification of human tissue-specific interactomes.

PubMed

Mohammadi, Shahin; Grama, Ananth

2016-06-15

Analysis of organism-specific interactomes has yielded novel insights into cellular function and coordination, understanding of pathology, and identification of markers and drug targets. Genes, however, can exhibit varying levels of cell type specificity in their expression, and their coordinated expression manifests in tissue-specific function and pathology. Tissue-specific/tissue-selective interaction mechanisms have significant applications in drug discovery, as they are more likely to reveal drug targets. Furthermore, tissue-specific transcription factors (tsTFs) are significantly implicated in human disease, including cancers. Finally, disease genes and protein complexes have the tendency to be differentially expressed in tissues in which defects cause pathology. These observations motivate the construction of refined tissue-specific interactomes from organism-specific interactomes. We present a novel technique for constructing human tissue-specific interactomes. Using a variety of validation tests (Edge Set Enrichment Analysis, Gene Ontology Enrichment, Disease-Gene Subnetwork Compactness), we show that our proposed approach significantly outperforms state-of-the-art techniques. Finally, using case studies of Alzheimer's and Parkinson's diseases, we show that tissue-specific interactomes derived from our study can be used to construct pathways implicated in pathology and demonstrate the use of these pathways in identifying novel targets. http://www.cs.purdue.edu/homes/mohammas/projects/ActPro.html mohammadi@purdue.edu. © The Author 2016. Published by Oxford University Press.

Bi-Level Integrated System Synthesis (BLISS) for Concurrent and Distributed Processing

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Altus, Troy D.; Phillips, Matthew; Sandusky, Robert

2002-01-01

The paper introduces a new version of the Bi-Level Integrated System Synthesis (BLISS) methods intended for optimization of engineering systems conducted by distributed specialty groups working concurrently and using a multiprocessor computing environment. The method decomposes the overall optimization task into subtasks associated with disciplines or subsystems where the local design variables are numerous and a single, system-level optimization whose design variables are relatively few. The subtasks are fully autonomous as to their inner operations and decision making. Their purpose is to eliminate the local design variables and generate a wide spectrum of feasible designs whose behavior is represented by Response Surfaces to be accessed by a system-level optimization. It is shown that, if the problem is convex, the solution of the decomposed problem is the same as that obtained without decomposition. A simplified example of an aircraft design shows the method working as intended. The paper includes a discussion of the method merits and demerits and recommendations for further research.

Profiling charge complementarity and selectivity for binding at the protein surface.

PubMed

Sulea, Traian; Purisima, Enrico O

2003-05-01

A novel analysis and representation of the protein surface in terms of electrostatic binding complementarity and selectivity is presented. The charge optimization methodology is applied in a probe-based approach that simulates the binding process to the target protein. The molecular surface is color coded according to calculated optimal charge or according to charge selectivity, i.e., the binding cost of deviating from the optimal charge. The optimal charge profile depends on both the protein shape and charge distribution whereas the charge selectivity profile depends only on protein shape. High selectivity is concentrated in well-shaped concave pockets, whereas solvent-exposed convex regions are not charge selective. This suggests the synergy of charge and shape selectivity hot spots toward molecular selection and recognition, as well as the asymmetry of charge selectivity at the binding interface of biomolecular systems. The charge complementarity and selectivity profiles map relevant electrostatic properties in a readily interpretable way and encode information that is quite different from that visualized in the standard electrostatic potential map of unbound proteins.

Design optimization of the S-frame to improve crashworthiness

NASA Astrophysics Data System (ADS)

Liu, Shu-Tian; Tong, Ze-Qi; Tang, Zhi-Liang; Zhang, Zong-Hua

2014-08-01

In this paper, the S-frames, the front side rail structures of automobile, were investigated for crashworthiness. Various cross-sections including regular polygon, non-convex polygon and multi-cell with inner stiffener sections were investigated in terms of energy absorption of S-frames. It was determined through extensive numerical simulation that a multi-cell S-frame with double vertical internal stiffeners can absorb more energy than the other configurations. Shape optimization was also carried out to improve energy absorption of the S-frame with a rectangular section. The center composite design of experiment and the sequential response surface method (SRSM) were adopted to construct the approximate design sub-problem, which was then solved by the feasible direction method. An innovative double S-frame was obtained from the optimal result. The optimum configuration of the S-frame was crushed numerically and more plastic hinges as well as shear zones were observed during the crush process. The energy absorption efficiency of the structure with the optimal configuration was improved compared to the initial configuration.

Optimal bounds and extremal trajectories for time averages in dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles

2017-11-01

For systems governed by differential equations it is natural to seek extremal solution trajectories, maximizing or minimizing the long-time average of a given quantity of interest. A priori bounds on optima can be proved by constructing auxiliary functions satisfying certain point-wise inequalities, the verification of which does not require solving the underlying equations. We prove that for any bounded autonomous ODE, the problems of finding extremal trajectories on the one hand and optimal auxiliary functions on the other are strongly dual in the sense of convex duality. As a result, auxiliary functions provide arbitrarily sharp bounds on optimal time averages. Furthermore, nearly optimal auxiliary functions provide volumes in phase space where maximal and nearly maximal trajectories must lie. For polynomial systems, such functions can be constructed by semidefinite programming. We illustrate these ideas using the Lorenz system, producing explicit volumes in phase space where extremal trajectories are guaranteed to reside. Supported by NSF Award DMS-1515161, Van Loo Postdoctoral Fellowships, and the John Simon Guggenheim Foundation.

Meshes optimized for discrete exterior calculus (DEC).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mousley, Sarah C.; Deakin, Michael; Knupp, Patrick

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximationmore » of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.« less

FSMRank: feature selection algorithm for learning to rank.

PubMed

Lai, Han-Jiang; Pan, Yan; Tang, Yong; Yu, Rong

2013-06-01

In recent years, there has been growing interest in learning to rank. The introduction of feature selection into different learning problems has been proven effective. These facts motivate us to investigate the problem of feature selection for learning to rank. We propose a joint convex optimization formulation which minimizes ranking errors while simultaneously conducting feature selection. This optimization formulation provides a flexible framework in which we can easily incorporate various importance measures and similarity measures of the features. To solve this optimization problem, we use the Nesterov's approach to derive an accelerated gradient algorithm with a fast convergence rate O(1/T(2)). We further develop a generalization bound for the proposed optimization problem using the Rademacher complexities. Extensive experimental evaluations are conducted on the public LETOR benchmark datasets. The results demonstrate that the proposed method shows: 1) significant ranking performance gain compared to several feature selection baselines for ranking, and 2) very competitive performance compared to several state-of-the-art learning-to-rank algorithms.

Charging, power management, and battery degradation mitigation in plug-in hybrid electric vehicles: A unified cost-optimal approach

NASA Astrophysics Data System (ADS)

Hu, Xiaosong; Martinez, Clara Marina; Yang, Yalian

2017-03-01

Holistic energy management of plug-in hybrid electric vehicles (PHEVs) in smart grid environment constitutes an enormous control challenge. This paper responds to this challenge by investigating the interactions among three important control tasks, i.e., charging, on-road power management, and battery degradation mitigation, in PHEVs. Three notable original contributions distinguish our work from existing endeavors. First, a new convex programming (CP)-based cost-optimal control framework is constructed to minimize the daily operational expense of a PHEV, which seamlessly integrates costs of the three tasks. Second, a straightforward but useful sensitivity assessment of the optimization outcome is executed with respect to price changes of battery and energy carriers. The potential impact of vehicle-to-grid (V2G) power flow on the PHEV economy is eventually analyzed through a multitude of comparative studies.

Global optimization algorithm for heat exchanger networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quesada, I.; Grossmann, I.E.

This paper deals with the global optimization of heat exchanger networks with fixed topology. It is shown that if linear area cost functions are assumed, as well as arithmetic mean driving force temperature differences in networks with isothermal mixing, the corresponding nonlinear programming (NLP) optimization problem involves linear constraints and a sum of linear fractional functions in the objective which are nonconvex. A rigorous algorithm is proposed that is based on a convex NLP underestimator that involves linear and nonlinear estimators for fractional and bilinear terms which provide a tight lower bound to the global optimum. This NLP problem ismore » used within a spatial branch and bound method for which branching rules are given. Basic properties of the proposed method are presented, and its application is illustrated with several example problems. The results show that the proposed method only requires few nodes in the branch and bound search.« less

Path Following in the Exact Penalty Method of Convex Programming.

PubMed

Zhou, Hua; Lange, Kenneth

2015-07-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

Path Following in the Exact Penalty Method of Convex Programming

PubMed Central

Zhou, Hua; Lange, Kenneth

2015-01-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

A fast optimization algorithm for multicriteria intensity modulated proton therapy planning.

PubMed

Chen, Wei; Craft, David; Madden, Thomas M; Zhang, Kewu; Kooy, Hanne M; Herman, Gabor T

2010-09-01

To describe a fast projection algorithm for optimizing intensity modulated proton therapy (IMPT) plans and to describe and demonstrate the use of this algorithm in multicriteria IMPT planning. The authors develop a projection-based solver for a class of convex optimization problems and apply it to IMPT treatment planning. The speed of the solver permits its use in multicriteria optimization, where several optimizations are performed which span the space of possible treatment plans. The authors describe a plan database generation procedure which is customized to the requirements of the solver. The optimality precision of the solver can be specified by the user. The authors apply the algorithm to three clinical cases: A pancreas case, an esophagus case, and a tumor along the rib cage case. Detailed analysis of the pancreas case shows that the algorithm is orders of magnitude faster than industry-standard general purpose algorithms (MOSEK'S interior point optimizer, primal simplex optimizer, and dual simplex optimizer). Additionally, the projection solver has almost no memory overhead. The speed and guaranteed accuracy of the algorithm make it suitable for use in multicriteria treatment planning, which requires the computation of several diverse treatment plans. Additionally, given the low memory overhead of the algorithm, the method can be extended to include multiple geometric instances and proton range possibilities, for robust optimization.

Probabilistic Guidance of Swarms using Sequential Convex Programming

DTIC Science & Technology

2014-01-01

quadcopter fleet [24]. In this paper, sequential convex programming (SCP) [25] is implemented using model predictive control (MPC) to provide real-time...in order to make Problem 1 convex. The details for convexifying this problem can be found in [26]. The main steps are discretizing the problem using

Rapid figure-ground responses to stereograms reveal an advantage for a convex foreground.

PubMed

Bertamini, Marco; Lawson, Rebecca

2008-01-01

Convexity has long been recognised as a factor that affects figure - ground segmentation, even when pitted against other factors such as symmetry [Kanizsa and Gerbino, 1976 Art and Artefacts Ed.M Henle (New York: Springer) pp 25-32]. It is accepted in the literature that the difference between concave and convex contours is important for the visual system, and that there is a prior expectation favouring convexities as figure. We used bipartite stimuli and a simple task in which observers had to report whether the foreground was on the left or the right. We report objective evidence that supports the idea that convexity affects figure-ground assignment, even though our stimuli were not pictorial in that depth order was specified unambiguously by binocular disparity.

Efficient computation of optimal actions.

PubMed

Todorov, Emanuel

2009-07-14

Optimal choice of actions is a fundamental problem relevant to fields as diverse as neuroscience, psychology, economics, computer science, and control engineering. Despite this broad relevance the abstract setting is similar: we have an agent choosing actions over time, an uncertain dynamical system whose state is affected by those actions, and a performance criterion that the agent seeks to optimize. Solving problems of this kind remains hard, in part, because of overly generic formulations. Here, we propose a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains. An exhaustive search over actions is avoided and the problem becomes linear. This yields algorithms that outperform Dynamic Programming and Reinforcement Learning, and thereby solve traditional problems more efficiently. Our framework also enables computations that were not possible before: composing optimal control laws by mixing primitives, applying deterministic methods to stochastic systems, quantifying the benefits of error tolerance, and inferring goals from behavioral data via convex optimization. Development of a general class of easily solvable problems tends to accelerate progress--as linear systems theory has done, for example. Our framework may have similar impact in fields where optimal choice of actions is relevant.

Joint global optimization of tomographic data based on particle swarm optimization and decision theory

NASA Astrophysics Data System (ADS)

Paasche, H.; Tronicke, J.

2012-04-01

In many near surface geophysical applications multiple tomographic data sets are routinely acquired to explore subsurface structures and parameters. Linking the model generation process of multi-method geophysical data sets can significantly reduce ambiguities in geophysical data analysis and model interpretation. Most geophysical inversion approaches rely on local search optimization methods used to find an optimal model in the vicinity of a user-given starting model. The final solution may critically depend on the initial model. Alternatively, global optimization (GO) methods have been used to invert geophysical data. They explore the solution space in more detail and determine the optimal model independently from the starting model. Additionally, they can be used to find sets of optimal models allowing a further analysis of model parameter uncertainties. Here we employ particle swarm optimization (PSO) to realize the global optimization of tomographic data. PSO is an emergent methods based on swarm intelligence characterized by fast and robust convergence towards optimal solutions. The fundamental principle of PSO is inspired by nature, since the algorithm mimics the behavior of a flock of birds searching food in a search space. In PSO, a number of particles cruise a multi-dimensional solution space striving to find optimal model solutions explaining the acquired data. The particles communicate their positions and success and direct their movement according to the position of the currently most successful particle of the swarm. The success of a particle, i.e. the quality of the currently found model by a particle, must be uniquely quantifiable to identify the swarm leader. When jointly inverting disparate data sets, the optimization solution has to satisfy multiple optimization objectives, at least one for each data set. Unique determination of the most successful particle currently leading the swarm is not possible. Instead, only statements about the Pareto optimality of the found solutions can be made. Identification of the leading particle traditionally requires a costly combination of ranking and niching techniques. In our approach, we use a decision rule under uncertainty to identify the currently leading particle of the swarm. In doing so, we consider the different objectives of our optimization problem as competing agents with partially conflicting interests. Analysis of the maximin fitness function allows for robust and cheap identification of the currently leading particle. The final optimization result comprises a set of possible models spread along the Pareto front. For convex Pareto fronts, solution density is expected to be maximal in the region ideally compromising all objectives, i.e. the region of highest curvature.

A Novel Semi-Supervised Methodology for Extracting Tumor Type-Specific MRS Sources in Human Brain Data

PubMed Central

Ortega-Martorell, Sandra; Ruiz, Héctor; Vellido, Alfredo; Olier, Iván; Romero, Enrique; Julià-Sapé, Margarida; Martín, José D.; Jarman, Ian H.; Arús, Carles; Lisboa, Paulo J. G.

2013-01-01

Background The clinical investigation of human brain tumors often starts with a non-invasive imaging study, providing information about the tumor extent and location, but little insight into the biochemistry of the analyzed tissue. Magnetic Resonance Spectroscopy can complement imaging by supplying a metabolic fingerprint of the tissue. This study analyzes single-voxel magnetic resonance spectra, which represent signal information in the frequency domain. Given that a single voxel may contain a heterogeneous mix of tissues, signal source identification is a relevant challenge for the problem of tumor type classification from the spectroscopic signal. Methodology/Principal Findings Non-negative matrix factorization techniques have recently shown their potential for the identification of meaningful sources from brain tissue spectroscopy data. In this study, we use a convex variant of these methods that is capable of handling negatively-valued data and generating sources that can be interpreted as tumor class prototypes. A novel approach to convex non-negative matrix factorization is proposed, in which prior knowledge about class information is utilized in model optimization. Class-specific information is integrated into this semi-supervised process by setting the metric of a latent variable space where the matrix factorization is carried out. The reported experimental study comprises 196 cases from different tumor types drawn from two international, multi-center databases. The results indicate that the proposed approach outperforms a purely unsupervised process by achieving near perfect correlation of the extracted sources with the mean spectra of the tumor types. It also improves tissue type classification. Conclusions/Significance We show that source extraction by unsupervised matrix factorization benefits from the integration of the available class information, so operating in a semi-supervised learning manner, for discriminative source identification and brain tumor labeling from single-voxel spectroscopy data. We are confident that the proposed methodology has wider applicability for biomedical signal processing. PMID:24376744

Earthquake Damage Assessment Using Objective Image Segmentation: A Case Study of 2010 Haiti Earthquake

NASA Technical Reports Server (NTRS)

Oommen, Thomas; Rebbapragada, Umaa; Cerminaro, Daniel

2012-01-01

In this study, we perform a case study on imagery from the Haiti earthquake that evaluates a novel object-based approach for characterizing earthquake induced surface effects of liquefaction against a traditional pixel based change technique. Our technique, which combines object-oriented change detection with discriminant/categorical functions, shows the power of distinguishing earthquake-induced surface effects from changes in buildings using the object properties concavity, convexity, orthogonality and rectangularity. Our results suggest that object-based analysis holds promise in automatically extracting earthquake-induced damages from high-resolution aerial/satellite imagery.

Radar/Sonar and Time Series Analysis

DTIC Science & Technology

1991-04-08

Fourier and Likelihood Analysis in NMR Spectroscopy .......... David Brillinger and Reinhold Kaiser Resampling Techniques for Stationary Time-series... Meyer The parabolic Fock theory foi a convex dielectric Georgia Tech. scatterer Abstract. This talk deals with a high frequency as) mptotic m~thod for...Malesky Inst. of Physics, Moscow Jun 11 - Jun 15 Victor P. Maslov MIEIM, USSR May 29 - Jun 15 Robert P. Meyer University of Wisconsin Jun 11 - Jun 15

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy; Saini, Subhash (Technical Monitor)

1999-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Energy Efficiency Optimization in Relay-Assisted MIMO Systems With Perfect and Statistical CSI

NASA Astrophysics Data System (ADS)

Zappone, Alessio; Cao, Pan; Jorswieck, Eduard A.

2014-01-01

A framework for energy-efficient resource allocation in a single-user, amplify-and-forward relay-assisted MIMO system is devised in this paper. Previous results in this area have focused on rate maximization or sum power minimization problems, whereas fewer results are available when bits/Joule energy efficiency (EE) optimization is the goal. The performance metric to optimize is the ratio between the system's achievable rate and the total consumed power. The optimization is carried out with respect to the source and relay precoding matrices, subject to QoS and power constraints. Such a challenging non-convex problem is tackled by means of fractional programming and and alternating maximization algorithms, for various CSI assumptions at the source and relay. In particular the scenarios of perfect CSI and those of statistical CSI for either the source-relay or the relay-destination channel are addressed. Moreover, sufficient conditions for beamforming optimality are derived, which is useful in simplifying the system design. Numerical results are provided to corroborate the validity of the theoretical findings.

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

Endobronchial ultrasound elastography: a new method in endobronchial ultrasound-guided transbronchial needle aspiration.

PubMed

Jiang, Jun-Hong; Turner, J Francis; Huang, Jian-An

2015-12-01

TBNA through the flexible bronchoscope is a 37-year-old technology that utilizes a TBNA needle to puncture the bronchial wall and obtain specimens of peribronchial and mediastinal lesions through the flexible bronchoscope for the diagnosis of benign and malignant diseases in the mediastinum and lung. Since 2002, the Olympus Company developed the first generation ultrasound equipment for use in the airway, initially utilizing an ultrasound probe introduced through the working channel followed by incoroporation of a fixed linear ultrasound array at the distal tip of the bronchoscope. This new bronchoscope equipped with a convex type ultrasound probe on the tip was subsequently introduced into clinical practice. The convex probe (CP)-EBUS allows real-time endobronchial ultrasound-guided transbronchial needle aspiration (EBUS-TBNA) of mediastinal and hilar lymph nodes. EBUS-TBNA is a minimally invasive procedure performed under local anesthesia that has been shown to have a high sensitivity and diagnostic yield for lymph node staging of lung cancer. In 10 years of EBUS development, the Olympus Company developed the second generation EBUS bronchoscope (BF-UC260FW) with the ultrasound image processor (EU-M1), and in 2013 introduced a new ultrasound image processor (EU-M2) into clinical practice. FUJI company has also developed a curvilinear array endobronchial ultrasound bronchoscope (EB-530 US) that makes it easier for the operator to master the operation of the ultrasonic bronchoscope. Also, the new thin convex probe endobronchial ultrasound bronchoscope (TCP-EBUS) is able to visualize one to three bifurcations distal to the current CP-EBUS. The emergence of EBUS-TBNA has also been accompanied by innovation in EBUS instruments. EBUS elastography is, then, a new technique for describing the compliance of structures during EBUS, which may be of use in the determination of metastasis to the mediastinal and hilar lymph nodes. This article describes these new EBUS techniques and reviews the relevant literature.

The Cartilage Warp Prevention Suture.

PubMed

Guyuron, Bahman; Wang, Derek Z; Kurlander, David E

2018-06-01

Costal cartilage graft warping can challenge rhinoplasty surgeons and compromise outcomes. We propose a technique, the "warp control suture," for eliminating cartilage warp and examine outcomes in a pilot group. The warp control suture is performed in the following manner: Harvested cartilage is cut to the desired shape and immersed in saline to induce warping. A 4-0 or 5-0 PDS suture, depending the thickness of the cartilage, is passed from convex to concave then concave to convex side several times about 5-6 mm apart, finally tying the suture on the convex side with sufficient tension to straighten the cartilage. First an ex vivo experiment was performed in 10 specimens from 10 different patients. Excess cartilage was sutured and returned to saline for a minimum of 15 min and then assessed for warping compared to cartilage cut in the identical shape also soaked in saline. Then, charts of nine subsequent patients who received the warp control suture on 16 cartilage grafts by the senior author (BG) were retrospectively reviewed. Inclusion of study subjects required at least 6 months of follow-up with standard rhinoplasty photographs. Postoperative complications and evidence of warping were recorded. In the ex vivo experiment, none of the 10 segments demonstrated warping after replacement in saline, whereas all the matching segments demonstrated significant additional warping. Clinically, no postoperative warping was observed in any of the nine patients at least 6 months postoperatively. One case of minor infection was observed in an area away from the graft and treated with antibiotics. No warping or other complications were noted. The warp control suture technique presented here effectively straightens warped cartilage graft and prevents additional warping. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .