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.

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.

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

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.

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.

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.

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

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.

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.

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.

PubMed

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

PubMed Central

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

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.

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).

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.

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.

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

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 .

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

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).

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.

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

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

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

String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images

NASA Astrophysics Data System (ADS)

Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo

2016-11-01

We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.

Convex central configurations for the n-body problem

NASA Astrophysics Data System (ADS)

Xia, Zhihong

We give a simple proof of a classical result of MacMillan and Bartky (Trans. Amer. Math. Soc. 34 (1932) 838) which states that, for any four positive masses and any assigned order, there is a convex planar central configuration. Moreover, we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia. This allows us to show that there are at least six local minimum central configurations for the planar four-body problem. We also show that for any assigned order of five masses, there is at least one convex spatial central configuration of local minimum type. Our method also applies to some other cases.

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

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 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

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

Point-in-convex polygon and point-in-convex polyhedron algorithms with O(1) complexity using space subdivision

NASA Astrophysics Data System (ADS)

Skala, Vaclav

2016-06-01

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 E2 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 E3 case, the complexity is O(N) even for the convex polyhedron as no ordering 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.

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.

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.

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

Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization

NASA Astrophysics Data System (ADS)

Adhikari, Sam

2007-11-01

Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.

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.

Convex optimisation approach to constrained fuel optimal control of spacecraft in close relative motion

NASA Astrophysics Data System (ADS)

Massioni, Paolo; Massari, Mauro

2018-05-01

This paper describes an interesting and powerful approach to the constrained fuel-optimal control of spacecraft in close relative motion. The proposed approach is well suited for problems under linear dynamic equations, therefore perfectly fitting to the case of spacecraft flying in close relative motion. If the solution of the optimisation is approximated as a polynomial with respect to the time variable, then the problem can be approached with a technique developed in the control engineering community, known as "Sum Of Squares" (SOS), and the constraints can be reduced to bounds on the polynomials. Such a technique allows rewriting polynomial bounding problems in the form of convex optimisation problems, at the cost of a certain amount of conservatism. The principles of the techniques are explained and some application related to spacecraft flying in close relative motion are shown.

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

Higher order sensitivity of solutions to convex programming problems without strict complementarity

NASA Technical Reports Server (NTRS)

Malanowski, Kazimierz

1988-01-01

Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.

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].

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.

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

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

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces.

PubMed

Butnariu, Dan; Censor, Yair; Gurfil, Pini; Hadar, Ethan

2008-07-03

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm's behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.

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.

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

PubMed Central

Butnariu, Dan; Censor, Yair; Gurfil, Pini; Hadar, Ethan

2010-01-01

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm’s behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method. PMID:20182556

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

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.

Image deblurring based on nonlocal regularization with a non-convex sparsity constraint

NASA Astrophysics Data System (ADS)

Zhu, Simiao; Su, Zhenming; Li, Lian; Yang, Yi

2018-04-01

In recent years, nonlocal regularization methods for image restoration (IR) have drawn more and more attention due to the promising results obtained when compared to the traditional local regularization methods. Despite the success of this technique, in order to obtain computational efficiency, a convex regularizing functional is exploited in most existing methods, which is equivalent to imposing a convex prior on the nonlocal difference operator output. However, our conducted experiment illustrates that the empirical distribution of the output of the nonlocal difference operator especially in the seminal work of Kheradmand et al. should be characterized with an extremely heavy-tailed distribution rather than a convex distribution. Therefore, in this paper, we propose a nonlocal regularization-based method with a non-convex sparsity constraint for image deblurring. Finally, an effective algorithm is developed to solve the corresponding non-convex optimization problem. The experimental results demonstrate the effectiveness of the proposed method.

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

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.

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.

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.

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

The roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems.

PubMed

Vickers, Douglas; Lee, Michael D; Dry, Matthew; Hughes, Peter

2003-10-01

The planar Euclidean version of the traveling salesperson problem requires finding the shortest tour through a two-dimensional array of points. MacGregor and Ormerod (1996) have suggested that people solve such problems by using a global-to-local perceptual organizing process based on the convex hull of the array. We review evidence for and against this idea, before considering an alternative, local-to-global perceptual process, based on the rapid automatic identification of nearest neighbors. We compare these approaches in an experiment in which the effects of number of convex hull points and number of potential intersections on solution performance are measured. Performance worsened with more points on the convex hull and with fewer potential intersections. A measure of response uncertainty was unaffected by the number of convex hull points but increased with fewer potential intersections. We discuss a possible interpretation of these results in terms of a hierarchical solution process based on linking nearest neighbor clusters.

End-point controller design for an experimental two-link flexible manipulator using convex optimization

NASA Technical Reports Server (NTRS)

Oakley, Celia M.; Barratt, Craig H.

1990-01-01

Recent results in linear controller design are used to design an end-point controller for an experimental two-link flexible manipulator. A nominal 14-state linear-quadratic-Gaussian (LQG) controller was augmented with a 528-tap finite-impulse-response (FIR) filter designed using convex optimization techniques. The resulting 278-state controller produced improved end-point trajectory tracking and disturbance rejection in simulation and experimentally in real time.

[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

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.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

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

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.

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

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.

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.

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

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.

Parallel-vector computation for structural analysis and nonlinear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1990-01-01

Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.

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

Tunneling and speedup in quantum optimization for permutation-symmetric problems

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

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final costmore » function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

Tunneling and speedup in quantum optimization for permutation-symmetric problems

DOE PAGES

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

2016-07-21

Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final costmore » function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

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.

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

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.

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.

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.

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.

The Lp Robin problem for Laplace equations in Lipschitz and (semi-)convex domains

NASA Astrophysics Data System (ADS)

Yang, Sibei; Yang, Dachun; Yuan, Wen

2018-01-01

Let n ≥ 3 and Ω be a bounded Lipschitz domain in Rn. Assume that p ∈ (2 , ∞) and the function b ∈L∞ (∂ Ω) is non-negative, where ∂Ω denotes the boundary of Ω. Denote by ν the outward unit normal to ∂Ω. In this article, the authors give two necessary and sufficient conditions for the unique solvability of the Robin problem for the Laplace equation Δu = 0 in Ω with boundary data ∂ u / ∂ ν + bu = f ∈Lp (∂ Ω), respectively, in terms of a weak reverse Hölder inequality with exponent p or the unique solvability of the Robin problem with boundary data in some weighted L2 (∂ Ω) space. As applications, the authors obtain the unique solvability of the Robin problem for the Laplace equation in the bounded (semi-)convex domain Ω with boundary data in (weighted) Lp (∂ Ω) for any given p ∈ (1 , ∞).

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

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

Optimal Micropatterns in 2D Transport Networks and Their Relation to Image Inpainting

NASA Astrophysics Data System (ADS)

Brancolini, Alessio; Rossmanith, Carolin; Wirth, Benedikt

2018-04-01

We consider two different variational models of transport networks: the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field, we show for a two-dimensional situation that both highly non-convex network optimization tasks can be transformed into a convex variational problem, which may be very useful from analytical and numerical perspectives. As applications of the convex formulation, we use it to perform numerical simulations (to our knowledge this is the first numerical treatment of urban planning), and we prove a lower bound for the network cost that matches a known upper bound (in terms of how the cost scales in the model parameters) which helps better understand optimal networks and their minimal costs.

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 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.

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

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.

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.

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.

Robust boosting via convex optimization

NASA Astrophysics Data System (ADS)

Rätsch, Gunnar

2001-12-01

In this work we consider statistical learning problems. A learning machine aims to extract information from a set of training examples such that it is able to predict the associated label on unseen examples. We consider the case where the resulting classification or regression rule is a combination of simple rules - also called base hypotheses. The so-called boosting algorithms iteratively find a weighted linear combination of base hypotheses that predict well on unseen data. We address the following issues: o The statistical learning theory framework for analyzing boosting methods. We study learning theoretic guarantees on the prediction performance on unseen examples. Recently, large margin classification techniques emerged as a practical result of the theory of generalization, in particular Boosting and Support Vector Machines. A large margin implies a good generalization performance. Hence, we analyze how large the margins in boosting are and find an improved algorithm that is able to generate the maximum margin solution. o How can boosting methods be related to mathematical optimization techniques? To analyze the properties of the resulting classification or regression rule, it is of high importance to understand whether and under which conditions boosting converges. We show that boosting can be used to solve large scale constrained optimization problems, whose solutions are well characterizable. To show this, we relate boosting methods to methods known from mathematical optimization, and derive convergence guarantees for a quite general family of boosting algorithms. o How to make Boosting noise robust? One of the problems of current boosting techniques is that they are sensitive to noise in the training sample. In order to make boosting robust, we transfer the soft margin idea from support vector learning to boosting. We develop theoretically motivated regularized algorithms that exhibit a high noise robustness. o How to adapt boosting to regression problems

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.

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.

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

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.

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.

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.

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

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.

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.

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.

Second-order optimality conditions for problems with C1 data

NASA Astrophysics Data System (ADS)

Ginchev, Ivan; Ivanov, Vsevolod I.

2008-04-01

In this paper we obtain second-order optimality conditions of Karush-Kuhn-Tucker type and Fritz John one for a problem with inequality constraints and a set constraint in nonsmooth settings using second-order directional derivatives. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable, but their gradients are not necessarily locally Lipschitz. In the sufficient conditions for a global minimum we assume that the objective function is differentiable at and second-order pseudoconvex at , a notion introduced by the authors [I. Ginchev, V.I. Ivanov, Higher-order pseudoconvex functions, in: I.V. Konnov, D.T. Luc, A.M. Rubinov (Eds.), Generalized Convexity and Related Topics, in: Lecture Notes in Econom. and Math. Systems, vol. 583, Springer, 2007, pp. 247-264], the constraints are both differentiable and quasiconvex at . In the sufficient conditions for an isolated local minimum of order two we suppose that the problem belongs to the class C1,1. We show that they do not hold for C1 problems, which are not C1,1 ones. At last a new notion parabolic local minimum is defined and it is applied to extend the sufficient conditions for an isolated local minimum from problems with C1,1 data to problems with C1 one.

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

Some Tours Are More Equal than Others: The Convex-Hull Model Revisited with Lessons for Testing Models of the Traveling Salesperson Problem

ERIC Educational Resources Information Center

Tak, Susanne; Plaisier, Marco; van Rooij, Iris

2008-01-01

To explain human performance on the "Traveling Salesperson" problem (TSP), MacGregor, Ormerod, and Chronicle (2000) proposed that humans construct solutions according to the steps described by their convex-hull algorithm. Focusing on tour length as the dependent variable, and using only random or semirandom point sets, the authors…

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.

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

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.

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

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.

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

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.

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.

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.

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.

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

The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons

NASA Astrophysics Data System (ADS)

Kweon, Jae Ryong

2017-03-01

In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: {{{u}}={{w}}+nablaφ_R} with div w = 0 and a potential φ_R. Here w is the solution for the incompressible Stokes problem and φ_R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.

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

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

Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control

NASA Astrophysics Data System (ADS)

Kamyar, Reza

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to

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.

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.

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.

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.

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

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.

Class and Home Problems: Optimization Problems

ERIC Educational Resources Information Center

Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard

2011-01-01

Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

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.

Optimal perturbations for nonlinear systems using graph-based optimal transport

NASA Astrophysics Data System (ADS)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

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.

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.

Convex Clustering: An Attractive Alternative to Hierarchical Clustering

PubMed Central

Chen, Gary K.; Chi, Eric C.; Ranola, John Michael O.; Lange, Kenneth

2015-01-01

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/ PMID:25965340

Convex clustering: an attractive alternative to hierarchical clustering.

PubMed

Chen, Gary K; Chi, Eric C; Ranola, John Michael O; Lange, Kenneth

2015-05-01

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/.

People efficiently explore the solution space of the computationally intractable traveling salesman problem to find near-optimal tours.

PubMed

Acuña, Daniel E; Parada, Víctor

2010-07-29

Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution ("good" edges) were significantly more likely to stay than other edges ("bad" edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants "ran out of ideas." In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics.

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

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...

Distributed Nash Equilibrium Seeking for Generalized Convex Games with Shared Constraints

NASA Astrophysics Data System (ADS)

Sun, Chao; Hu, Guoqiang

2018-05-01

In this paper, we deal with the problem of finding a Nash equilibrium for a generalized convex game. Each player is associated with a convex cost function and multiple shared constraints. Supposing that each player can exchange information with its neighbors via a connected undirected graph, the objective of this paper is to design a Nash equilibrium seeking law such that each agent minimizes its objective function in a distributed way. Consensus and singular perturbation theories are used to prove the stability of the system. A numerical example is given to show the effectiveness of the proposed algorithms.

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.

Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations

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

Dvijotham, Krishnamurthy; Low, Steven; Chertkov, Michael

2015-01-12

Power systems are undergoing unprecedented transformations with increased adoption of renewables and distributed generation, as well as the adoption of demand response programs. All of these changes, while making the grid more responsive and potentially more efficient, pose significant challenges for power systems operators. Conventional operational paradigms are no longer sufficient as the power system may no longer have big dispatchable generators with sufficient positive and negative reserves. This increases the need for tools and algorithms that can efficiently predict safe regions of operation of the power system. In this paper, we study energy functions as a tool to designmore » algorithms for various operational problems in power systems. These have a long history in power systems and have been primarily applied to transient stability problems. In this paper, we take a new look at power systems, focusing on an aspect that has previously received little attention: Convexity. We characterize the domain of voltage magnitudes and phases within which the energy function is convex in these variables. We show that this corresponds naturally with standard operational constraints imposed in power systems. We show that power of equations can be solved using this approach, as long as the solution lies within the convexity domain. We outline various desirable properties of solutions in the convexity domain and present simple numerical illustrations supporting our results.« less

Modified surface testing method for large convex aspheric surfaces based on diffraction optics.

PubMed

Zhang, Haidong; Wang, Xiaokun; Xue, Donglin; Zhang, Xuejun

2017-12-01

Large convex aspheric optical elements have been widely applied in advanced optical systems, which have presented a challenging metrology problem. Conventional testing methods cannot satisfy the demand gradually with the change of definition of "large." A modified method is proposed in this paper, which utilizes a relatively small computer-generated hologram and an illumination lens with certain feasibility to measure the large convex aspherics. Two example systems are designed to demonstrate the applicability, and also, the sensitivity of this configuration is analyzed, which proves the accuracy of the configuration can be better than 6 nm with careful alignment and calibration of the illumination lens in advance. Design examples and analysis show that this configuration is applicable to measure the large convex aspheric surfaces.

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…

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.

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.

A parallel Discrete Element Method to model collisions between non-convex particles

NASA Astrophysics Data System (ADS)

Rakotonirina, Andriarimina Daniel; Delenne, Jean-Yves; Wachs, Anthony

2017-06-01

In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called "glued-convex method" (in the sense clumping convex bodies together), as an extension of the popular "glued-spheres" method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor.

COPS: Large-scale nonlinearly constrained optimization problems

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

Bondarenko, A.S.; Bortz, D.M.; More, J.J.

2000-02-10

The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.

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.

People Efficiently Explore the Solution Space of the Computationally Intractable Traveling Salesman Problem to Find Near-Optimal Tours

PubMed Central

Acuña, Daniel E.; Parada, Víctor

2010-01-01

Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution (“good” edges) were significantly more likely to stay than other edges (“bad” edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants “ran out of ideas.” In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics. PMID:20686597

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.

Convex set and linear mixing model

NASA Technical Reports Server (NTRS)

Xu, P.; Greeley, R.

1993-01-01

A major goal of optical remote sensing is to determine surface compositions of the earth and other planetary objects. For assessment of composition, single pixels in multi-spectral images usually record a mixture of the signals from various materials within the corresponding surface area. In this report, we introduce a closed and bounded convex set as a mathematical model for linear mixing. This model has a clear geometric implication because the closed and bounded convex set is a natural generalization of a triangle in n-space. The endmembers are extreme points of the convex set. Every point in the convex closure of the endmembers is a linear mixture of those endmembers, which is exactly how linear mixing is defined. With this model, some general criteria for selecting endmembers could be described. This model can lead to a better understanding of linear mixing models.

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems

NASA Astrophysics Data System (ADS)

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

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.

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 Problem on Optimal Transportation

ERIC Educational Resources Information Center

Cechlarova, Katarina

2005-01-01

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

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.

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.

The importance of the convex hull for human performance on the traveling salesman problem: a comment on MacGregor and Ormerod (1996)

PubMed

Lee, M D; Vickers, D

2000-01-01

MacGregor and Ormerod (1996) have presented results purporting to show that human performance on visually presented traveling salesman problems, as indexed by a measure of response uncertainty, is strongly determined by the number of points in the stimulus array falling inside the convex hull, as distinct from the total number of points. It is argued that this conclusion is artifactually determined by their constrained procedure for stimulus construction, and, even if true, would be limited to arrays with fewer than around 50 points.

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

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

Semidefinite Relaxation-Based Optimization of Multiple-Input Wireless Power Transfer Systems

NASA Astrophysics Data System (ADS)

Lang, Hans-Dieter; Sarris, Costas D.

2017-11-01

An optimization procedure for multi-transmitter (MISO) wireless power transfer (WPT) systems based on tight semidefinite relaxation (SDR) is presented. This method ensures physical realizability of MISO WPT systems designed via convex optimization -- a robust, semi-analytical and intuitive route to optimizing such systems. To that end, the nonconvex constraints requiring that power is fed into rather than drawn from the system via all transmitter ports are incorporated in a convex semidefinite relaxation, which is efficiently and reliably solvable by dedicated algorithms. A test of the solution then confirms that this modified problem is equivalent (tight relaxation) to the original (nonconvex) one and that the true global optimum has been found. This is a clear advantage over global optimization methods (e.g. genetic algorithms), where convergence to the true global optimum cannot be ensured or tested. Discussions of numerical results yielded by both the closed-form expressions and the refined technique illustrate the importance and practicability of the new method. It, is shown that this technique offers a rigorous optimization framework for a broad range of current and emerging WPT applications.

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

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.

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 .

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 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.

The Band around a Convex Body

ERIC Educational Resources Information Center

Swanson, David

2011-01-01

We give elementary proofs of formulas for the area and perimeter of a planar convex body surrounded by a band of uniform thickness. The primary tool is a integral formula for the perimeter of a convex body which describes the perimeter in terms of the projections of the body onto lines in the plane.

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

Problem Solving through an Optimization Problem in Geometry

ERIC Educational Resources Information Center

Poon, Kin Keung; Wong, Hang-Chi

2011-01-01

This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

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

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.

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.

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

Convexity of quantum χ2-divergence.

PubMed

Hansen, Frank

2011-06-21

The general quantum χ(2)-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ(2)-divergence is not unique, as opposed to the classical χ(2)-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family of quantum χ(2)-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ(2)(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ(2)-divergence is a convex function in its two arguments.

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

Binary optimization for source localization in the inverse problem of ECG.

PubMed

Potyagaylo, Danila; Cortés, Elisenda Gil; Schulze, Walther H W; Dössel, Olaf

2014-09-01

The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance.

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.

A Mathematical Optimization Problem in Bioinformatics

ERIC Educational Resources Information Center

Heyer, Laurie J.

2008-01-01

This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

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

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.

Performance of Grey Wolf Optimizer on large scale problems

NASA Astrophysics Data System (ADS)

Gupta, Shubham; Deep, Kusum

2017-01-01

For solving nonlinear continuous problems of optimization numerous nature inspired optimization techniques are being proposed in literature which can be implemented to solve real life problems wherein the conventional techniques cannot be applied. Grey Wolf Optimizer is one of such technique which is gaining popularity since the last two years. The objective of this paper is to investigate the performance of Grey Wolf Optimization Algorithm on large scale optimization problems. The Algorithm is implemented on 5 common scalable problems appearing in literature namely Sphere, Rosenbrock, Rastrigin, Ackley and Griewank Functions. The dimensions of these problems are varied from 50 to 1000. The results indicate that Grey Wolf Optimizer is a powerful nature inspired Optimization Algorithm for large scale problems, except Rosenbrock which is a unimodal function.

Computing convex quadrangulations☆

PubMed Central

Schiffer, T.; Aurenhammer, F.; Demuth, M.

2012-01-01

We use projected Delaunay tetrahedra and a maximum independent set approach to compute large subsets of convex quadrangulations on a given set of points in the plane. The new method improves over the popular pairing method based on triangulating the point set. PMID:22389540

A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

NASA Astrophysics Data System (ADS)

Sayed, Gehad Ismail; Darwish, Ashraf; Hassanien, Aboul Ella

2018-03-01

Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO's performance.

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

Solving optimization problems on computational grids.

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

Wright, S. J.; Mathematics and Computer Science

2001-05-01

Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms havemore » become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software

Comparison of Optimal Design Methods in Inverse Problems

PubMed Central

Banks, H. T.; Holm, Kathleen; Kappel, Franz

2011-01-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762

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.

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.

Optimality conditions for the numerical solution of optimization problems with PDE constraints :

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

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

SLOPE—ADAPTIVE VARIABLE SELECTION VIA CONVEX OPTIMIZATION

PubMed Central

Bogdan, Małgorzata; van den Berg, Ewout; Sabatti, Chiara; Su, Weijie; Candès, Emmanuel J.

2015-01-01

We introduce a new estimator for the vector of coefficients β in the linear model y = Xβ + z, where X has dimensions n × p with p possibly larger than n. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to minb∈ℝp12‖y−Xb‖ℓ22+λ1|b|(1)+λ2|b|(2)+⋯+λp|b|(p),where λ1 ≥ λ2 ≥ … ≥ λp ≥ 0 and |b|(1)≥|b|(2)≥⋯≥|b|(p) are the decreasing absolute values of the entries of b. This is a convex program and we demonstrate a solution algorithm whose computational complexity is roughly comparable to that of classical ℓ1 procedures such as the Lasso. Here, the regularizer is a sorted ℓ1 norm, which penalizes the regression coefficients according to their rank: the higher the rank—that is, stronger the signal—the larger the penalty. This is similar to the Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300] procedure (BH) which compares more significant p-values with more stringent thresholds. One notable choice of the sequence {λi} is given by the BH critical values λBH(i)=z(1−i⋅q/2p), where q ∈ (0, 1) and z(α) is the quantile of a standard normal distribution. SLOPE aims to provide finite sample guarantees on the selected model; of special interest is the false discovery rate (FDR), defined as the expected proportion of irrelevant regressors among all selected predictors. Under orthogonal designs, SLOPE with λBH provably controls FDR at level q. Moreover, it also appears to have appreciable inferential properties under more general designs X while having substantial power, as demonstrated in a series of experiments running on both simulated and real data. PMID:26709357

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.

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

Polar DuaLs of Convex Bodies

DTIC Science & Technology

1990-01-01

Verlag 1976. 17. C. G. Lekkerkerker, Geometry of Numbers, Wolters-Noordhoff, Groningen, 1969. 18. E . Lutwak , "Dual Mixed Volumes," Pacific Journal of...Mathematics, Vol. 58, No. 2, 1975. 19. E . Lutwak , "On Cross-Sectional Measures of Polar Reciprocal Convex Bodies," Geometriae Dedicata 5, (1976) 79-80...20. E . Lutwak , "Blaschke-Santal6 Inequality, Discrete Geometry and Convexity," Annals of the New York Academy of Sciences 440 (1985) pp 106-112. 21. V

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.

A convex penalty for switching control of partial differential equations

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

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

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.

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.

A linear programming approach to max-sum problem: a review.

PubMed

Werner, Tomás

2007-07-01

The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.

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

Optimal recombination in genetic algorithms for flowshop scheduling problems

NASA Astrophysics Data System (ADS)

Kovalenko, Julia

2016-10-01

The optimal recombination problem consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We prove NP-hardness of the optimal recombination for various variants of the flowshop scheduling problem with makespan criterion and criterion of maximum lateness. An algorithm for solving the optimal recombination problem for permutation flowshop problems is built, using enumeration of prefect matchings in a special bipartite graph. The algorithm is adopted for the classical flowshop scheduling problem and for the no-wait flowshop problem. It is shown that the optimal recombination problem for the permutation flowshop scheduling problem is solvable in polynomial time for almost all pairs of parent solutions as the number of jobs tends to infinity.

Stereotype locally convex spaces

NASA Astrophysics Data System (ADS)

Akbarov, S. S.

2000-08-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

A general optimality criteria algorithm for a class of engineering optimization problems

NASA Astrophysics Data System (ADS)

Belegundu, Ashok D.

2015-05-01

An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.

Entropy and convexity for nonlinear partial differential equations

PubMed Central

Ball, John M.; Chen, Gui-Qiang G.

2013-01-01

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

Entropy and convexity for nonlinear partial differential equations.

PubMed

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems.

PubMed

Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A

2014-01-01

This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.

The Coral Reefs Optimization Algorithm: A Novel Metaheuristic for Efficiently Solving Optimization Problems

PubMed Central

Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.

2014-01-01

This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860

On equivalent characterizations of convexity of functions

NASA Astrophysics Data System (ADS)

Gkioulekas, Eleftherios

2013-04-01

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

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.

Path optimization method for the sign problem

NASA Astrophysics Data System (ADS)

Ohnishi, Akira; Mori, Yuto; Kashiwa, Kouji

2018-03-01

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t)(f ɛ R) and by optimizing f(t) to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

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

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.

Direct Multiple Shooting Optimization with Variable Problem Parameters

NASA Technical Reports Server (NTRS)

Whitley, Ryan J.; Ocampo, Cesar A.

2009-01-01

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

LDRD Final Report: Global Optimization for Engineering Science Problems

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

HART,WILLIAM E.

1999-12-01

For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.

Distributed convex optimisation with event-triggered communication in networked systems

NASA Astrophysics Data System (ADS)

Liu, Jiayun; Chen, Weisheng

2016-12-01

This paper studies the distributed convex optimisation problem over directed networks. Motivated by practical considerations, we propose a novel distributed zero-gradient-sum optimisation algorithm with event-triggered communication. Therefore, communication and control updates just occur at discrete instants when some predefined condition satisfies. Thus, compared with the time-driven distributed optimisation algorithms, the proposed algorithm has the advantages of less energy consumption and less communication cost. Based on Lyapunov approaches, we show that the proposed algorithm makes the system states asymptotically converge to the solution of the problem exponentially fast and the Zeno behaviour is excluded. Finally, simulation example is given to illustrate the effectiveness of the proposed algorithm.

Building Energy Modeling and Control Methods for Optimization and Renewables Integration

NASA Astrophysics Data System (ADS)

Burger, Eric M.

dynamics within a building by learning from sensor data. Control techniques encompass the application of optimal control theory, model predictive control, and convex distributed optimization to TCLs. First, we present the alternative control trajectory (ACT) representation, a novel method for the approximate optimization of non-convex discrete systems. This approach enables the optimal control of a population of non-convex agents using distributed convex optimization techniques. Second, we present a distributed convex optimization algorithm for the control of a TCL population. Experimental results demonstrate the application of this algorithm to the problem of renewable energy generation following. This dissertation contributes to the development of intelligent energy management systems for buildings by presenting a suite of novel and adaptable modeling and control techniques. Applications focus on optimizing the performance of building operations and on facilitating the integration of renewable energy resources.

Evaluating convex roof entanglement measures.

PubMed

Tóth, Géza; Moroder, Tobias; Gühne, Otfried

2015-04-24

We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

Inhibitory competition in figure-ground perception: context and convexity.

PubMed

Peterson, Mary A; Salvagio, Elizabeth

2008-12-15

Convexity has long been considered a potent cue as to which of two regions on opposite sides of an edge is the shaped figure. Experiment 1 shows that for a single edge, there is only a weak bias toward seeing the figure on the convex side. Experiments 1-3 show that the bias toward seeing the convex side as figure increases as the number of edges delimiting alternating convex and concave regions increases, provided that the concave regions are homogeneous in color. The results of Experiments 2 and 3 rule out a probability summation explanation for these context effects. Taken together, the results of Experiments 1-3 show that the homogeneity versus heterogeneity of the convex regions is irrelevant. Experiment 4 shows that homogeneity of alternating regions is not sufficient for context effects; a cue that favors the perception of the intervening regions as figures is necessary. Thus homogeneity alone does not alone operate as a background cue. We interpret our results within a model of figure-ground perception in which shape properties on opposite sides of an edge compete for representation and the competitive strength of weak competitors is further reduced when they are homogeneous.

Convexities move because they contain matter.

PubMed

Barenholtz, Elan

2010-09-22

Figure-ground assignment to a contour is a fundamental stage in visual processing. The current paper introduces a novel, highly general dynamic cue to figure-ground assignment: "Convex Motion." Across six experiments, subjects showed a strong preference to assign figure and ground to a dynamically deforming contour such that the moving contour segment was convex rather than concave. Experiments 1 and 2 established the preference across two different kinds of deformational motion. Additional experiments determined that this preference was not due to fixation (Experiment 3) or attentional mechanisms (Experiment 4). Experiment 5 found a similar, but reduced bias for rigid-as opposed to deformational-motion, and Experiment 6 demonstrated that the phenomenon depends on the global motion of the effected contour. An explanation of this phenomenon is presented on the basis of typical natural deformational motion, which tends to involve convex contour projections that contain regions consisting of physical "matter," as opposed to concave contour indentations that contain empty space. These results highlight the fundamental relationship between figure and ground, perceived shape, and the inferred physical properties of an object.

Analog Processor To Solve Optimization Problems

NASA Technical Reports Server (NTRS)

Duong, Tuan A.; Eberhardt, Silvio P.; Thakoor, Anil P.

1993-01-01

Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.

FRANOPP: Framework for analysis and optimization problems user's guide

NASA Technical Reports Server (NTRS)

Riley, K. M.

1981-01-01

Framework for analysis and optimization problems (FRANOPP) is a software aid for the study and solution of design (optimization) problems which provides the driving program and plotting capability for a user generated programming system. In addition to FRANOPP, the programming system also contains the optimization code CONMIN, and two user supplied codes, one for analysis and one for output. With FRANOPP the user is provided with five options for studying a design problem. Three of the options utilize the plot capability and present an indepth study of the design problem. The study can be focused on a history of the optimization process or on the interaction of variables within the design problem.

Weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1991-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

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.

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.

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.

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

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.

Comparison of optimal design methods in inverse problems

NASA Astrophysics Data System (ADS)

Banks, H. T.; Holm, K.; Kappel, F.

2011-07-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

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.

An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems.

PubMed

Islam, Md Monjurul; Singh, Hemant Kumar; Ray, Tapabrata; Sinha, Ankur

2017-01-01

Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify the optimum of an upper-level  leader problem, subject to the optimality of a lower-level follower problem. Several problems from the domain of engineering, logistics, economics, and transportation have an inherent nested structure which requires them to be modeled as bilevel optimization problems. Increasing size and complexity of such problems has prompted active theoretical and practical interest in the design of efficient algorithms for bilevel optimization. Given the nested nature of bilevel problems, the computational effort (number of function evaluations) required to solve them is often quite high. In this article, we explore the use of a Memetic Algorithm (MA) to solve bilevel optimization problems. While MAs have been quite successful in solving single-level optimization problems, there have been relatively few studies exploring their potential for solving bilevel optimization problems. MAs essentially attempt to combine advantages of global and local search strategies to identify optimum solutions with low computational cost (function evaluations). The approach introduced in this article is a nested Bilevel Memetic Algorithm (BLMA). At both upper and lower levels, either a global or a local search method is used during different phases of the search. The performance of BLMA is presented on twenty-five standard test problems and two real-life applications. The results are compared with other established algorithms to demonstrate the efficacy of the proposed approach.

Global optimization methods for engineering design

NASA Technical Reports Server (NTRS)

Arora, Jasbir S.

1990-01-01

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

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.

Singular perturbation analysis of AOTV-related trajectory optimization problems

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Bae, Gyoung H.

1990-01-01

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality

Belief Propagation Algorithm for Portfolio Optimization Problems

PubMed Central

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462

Belief Propagation Algorithm for Portfolio Optimization Problems.

PubMed

Shinzato, Takashi; Yasuda, Muneki

2015-01-01

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

Convex geometry of quantum resource quantification

NASA Astrophysics Data System (ADS)

Regula, Bartosz

2018-01-01

We introduce a framework unifying the mathematical characterisation of different measures of general quantum resources and allowing for a systematic way to define a variety of faithful quantifiers for any given convex quantum resource theory. The approach allows us to describe many commonly used measures such as matrix norm-based quantifiers, robustness measures, convex roof-based measures, and witness-based quantifiers together in a common formalism based on the convex geometry of the underlying sets of resource-free states. We establish easily verifiable criteria for a measure to possess desirable properties such as faithfulness and strong monotonicity under relevant free operations, and show that many quantifiers obtained in this framework indeed satisfy them for any considered quantum resource. We derive various bounds and relations between the measures, generalising and providing significantly simplified proofs of results found in the resource theories of quantum entanglement and coherence. We also prove that the quantification of resources in this framework simplifies for pure states, allowing us to obtain more easily computable forms of the considered measures, and show that many of them are in fact equal on pure states. Further, we investigate the dual formulation of resource quantifiers, which provide a characterisation of the sets of resource witnesses. We present an explicit application of the results to the resource theories of multi-level coherence, entanglement of Schmidt number k, multipartite entanglement, as well as magic states, providing insight into the quantification of the four resources by establishing novel quantitative relations and introducing new quantifiers, such as a measure of entanglement of Schmidt number k which generalises the convex roof-extended negativity, a measure of k-coherence which generalises the \

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

DOE PAGES

Simonetto, Andrea; Dall'Anese, Emiliano

2017-07-26

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo

1996-01-01

A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.

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.

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

NASA Technical Reports Server (NTRS)

Balling, R. J.; Wilkinson, C. A.

1997-01-01

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

The optimization problems of CP operation

NASA Astrophysics Data System (ADS)

Kler, A. M.; Stepanova, E. L.; Maximov, A. S.

2017-11-01

The problem of enhancing energy and economic efficiency of CP is urgent indeed. One of the main methods for solving it is optimization of CP operation. To solve the optimization problems of CP operation, Energy Systems Institute, SB of RAS, has developed a software. The software makes it possible to make optimization calculations of CP operation. The software is based on the techniques and software tools of mathematical modeling and optimization of heat and power installations. Detailed mathematical models of new equipment have been developed in the work. They describe sufficiently accurately the processes that occur in the installations. The developed models include steam turbine models (based on the checking calculation) which take account of all steam turbine compartments and regeneration system. They also enable one to make calculations with regenerative heaters disconnected. The software for mathematical modeling of equipment and optimization of CP operation has been developed. It is based on the technique for optimization of CP operating conditions in the form of software tools and integrates them in the common user interface. The optimization of CP operation often generates the need to determine the minimum and maximum possible total useful electricity capacity of the plant at set heat loads of consumers, i.e. it is necessary to determine the interval on which the CP capacity may vary. The software has been applied to optimize the operating conditions of the Novo-Irkutskaya CP of JSC “Irkutskenergo”. The efficiency of operating condition optimization and the possibility for determination of CP energy characteristics that are necessary for optimization of power system operation are shown.

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.

The expanded invasive weed optimization metaheuristic for solving continuous and discrete optimization problems.

PubMed

Josiński, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Switoński, Adam

2014-01-01

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature.

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.

Random Matrix Approach for Primal-Dual Portfolio Optimization Problems

NASA Astrophysics Data System (ADS)

Tada, Daichi; Yamamoto, Hisashi; Shinzato, Takashi

2017-12-01

In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment concentration under constraints of budget and investment risk (dual problem) for the case that the variances of the return rates of the assets are identical. We analyze both optimization problems by the Lagrange multiplier method and the random matrix approach. Thereafter, we compare the results obtained from our proposed approach with the results obtained in previous work. Moreover, we use numerical experiments to validate the results obtained from the replica approach and the random matrix approach as methods for analyzing both the primal and dual portfolio optimization problems.

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.

Convexity and concavity constants in Lorentz and Marcinkiewicz spaces

NASA Astrophysics Data System (ADS)

Kaminska, Anna; Parrish, Anca M.

2008-07-01

We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kaminska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373].

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.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1989-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1990-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

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.

Optimal Price Decision Problem for Simultaneous Multi-article Auction and Its Optimal Price Searching Method by Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Masuda, Kazuaki; Aiyoshi, Eitaro

We propose a method for solving optimal price decision problems for simultaneous multi-article auctions. An auction problem, originally formulated as a combinatorial problem, determines both every seller's whether or not to sell his/her article and every buyer's which article(s) to buy, so that the total utility of buyers and sellers will be maximized. Due to the duality theory, we transform it equivalently into a dual problem in which Lagrange multipliers are interpreted as articles' transaction price. As the dual problem is a continuous optimization problem with respect to the multipliers (i.e., the transaction prices), we propose a numerical method to solve it by applying heuristic global search methods. In this paper, Particle Swarm Optimization (PSO) is used to solve the dual problem, and experimental results are presented to show the validity of the proposed method.

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.

Robust optimization modelling with applications to industry and environmental problems

NASA Astrophysics Data System (ADS)

Chaerani, Diah; Dewanto, Stanley P.; Lesmana, Eman

2017-10-01

Robust Optimization (RO) modeling is one of the existing methodology for handling data uncertainty in optimization problem. The main challenge in this RO methodology is how and when we can reformulate the robust counterpart of uncertain problems as a computationally tractable optimization problem or at least approximate the robust counterpart by a tractable problem. Due to its definition the robust counterpart highly depends on how we choose the uncertainty set. As a consequence we can meet this challenge only if this set is chosen in a suitable way. The development on RO grows fast, since 2004, a new approach of RO called Adjustable Robust Optimization (ARO) is introduced to handle uncertain problems when the decision variables must be decided as a ”wait and see” decision variables. Different than the classic Robust Optimization (RO) that models decision variables as ”here and now”. In ARO, the uncertain problems can be considered as a multistage decision problem, thus decision variables involved are now become the wait and see decision variables. In this paper we present the applications of both RO and ARO. We present briefly all results to strengthen the importance of RO and ARO in many real life problems.

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.

Image restoration by the method of convex projections: part 1 theory.

PubMed

Youla, D C; Webb, H

1982-01-01

A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically. Their common conceptual basis is as follows. Every known property of an original image f is envisaged as restricting it to lie in a well-defined closed convex set. Thus, m such properties place f in the intersection E(0) = E(i) of the corresponding closed convex sets E(1),E(2),...EE(m). Given only the projection operators PE(i) onto the individual E(i)'s, i = 1 --> m, we restore f by recursive means. Clearly, in this approach, the realization of the P(i)'s in a Hilbert space setting is one of the major synthesis problems. Section I describes the geometrical significance of the three main theorems in considerable detail, and most of the underlying ideas are illustrated with the aid of simple diagrams. Section II presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal-processing applications, and the Appendix contains proofs of all the major results.

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.

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games

DTIC Science & Technology

2016-05-01

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...subproblems. Our approach is expected to have wide applications in continuous dynamic games , control theory problems, and elsewhere. Mathematics...differential dynamic games , control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to

Transient disturbance growth in flows over convex surfaces

NASA Astrophysics Data System (ADS)

Karp, Michael; Hack, M. J. Philipp

2017-11-01

Flows over curved surfaces occur in a wide range of applications including airfoils, compressor and turbine vanes as well as aerial, naval and ground vehicles. In most of these applications the surface has convex curvature, while concave surfaces are less common. Since monotonic boundary-layer flows over convex surfaces are exponentially stable, they have received considerably less attention than flows over concave walls which are destabilized by centrifugal forces. Non-modal mechanisms may nonetheless enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instability of flows over convex surfaces is performed. The specific conditions yielding the maximal transient growth and strongest instability are identified. The effect of wall-normal and spanwise inflection points on the instability process is discussed. Finally, the role and significance of additional parameters, such as the geometry and pressure gradient, is analyzed.

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

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.

It looks easy! Heuristics for combinatorial optimization problems.

PubMed

Chronicle, Edward P; MacGregor, James N; Ormerod, Thomas C; Burr, Alistair

2006-04-01

Human performance on instances of computationally intractable optimization problems, such as the travelling salesperson problem (TSP), can be excellent. We have proposed a boundary-following heuristic to account for this finding. We report three experiments with TSPs where the capacity to employ this heuristic was varied. In Experiment 1, participants free to use the heuristic produced solutions significantly closer to optimal than did those prevented from doing so. Experiments 2 and 3 together replicated this finding in larger problems and demonstrated that a potential confound had no effect. In all three experiments, performance was closely matched by a boundary-following model. The results implicate global rather than purely local processes. Humans may have access to simple, perceptually based, heuristics that are suited to some combinatorial optimization tasks.

Forecasting Electricity Prices in an Optimization Hydrothermal Problem

NASA Astrophysics Data System (ADS)

Matías, J. M.; Bayón, L.; Suárez, P.; Argüelles, A.; Taboada, J.

2007-12-01

This paper presents an economic dispatch algorithm in a hydrothermal system within the framework of a competitive and deregulated electricity market. The optimization problem of one firm is described, whose objective function can be defined as its profit maximization. Since next-day price forecasting is an aspect crucial, this paper proposes an efficient yet highly accurate next-day price new forecasting method using a functional time series approach trying to exploit the daily seasonal structure of the series of prices. For the optimization problem, an optimal control technique is applied and Pontryagin's theorem is employed.

About an Optimal Visiting Problem

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

Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela

In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not,more » and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.« less

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

Essays on variational approximation techniques for stochastic optimization problems

NASA Astrophysics Data System (ADS)

Deride Silva, Julio A.

This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence

Replica analysis for the duality of the portfolio optimization problem

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2016-11-01

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

Replica analysis for the duality of the portfolio optimization problem.

PubMed

Shinzato, Takashi

2016-11-01

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

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

Kamm, James Russell

2015-03-05

This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equationmore » of state and for the JWL equation of state.« less

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.

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).

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.

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.

Determining Representative Elementary Volume For Multiple Petrophysical Parameters using a Convex Hull Analysis of Digital Rock Data

NASA Astrophysics Data System (ADS)

Shah, S.; Gray, F.; Yang, J.; Crawshaw, J.; Boek, E.

2016-12-01

Advances in 3D pore-scale imaging and computational methods have allowed an exceptionally detailed quantitative and qualitative analysis of the fluid flow in complex porous media. A fundamental problem in pore-scale imaging and modelling is how to represent and model the range of scales encountered in porous media, starting from the smallest pore spaces. In this study, a novel method is presented for determining the representative elementary volume (REV) of a rock for several parameters simultaneously. We calculate the two main macroscopic petrophysical parameters, porosity and single-phase permeability, using micro CT imaging and Lattice Boltzmann (LB) simulations for 14 different porous media, including sandpacks, sandstones and carbonates. The concept of the `Convex Hull' is then applied to calculate the REV for both parameters simultaneously using a plot of the area of the convex hull as a function of the sub-volume, capturing the different scales of heterogeneity from the pore-scale imaging. The results also show that the area of the convex hull (for well-chosen parameters such as the log of the permeability and the porosity) decays exponentially with sub-sample size suggesting a computationally efficient way to determine the system size needed to calculate the parameters to high accuracy (small convex hull area). Finally we propose using a characteristic length such as the pore size to choose an efficient absolute voxel size for the numerical rock.

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.

Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Janečka, Adam; Pavelka, Michal

2018-04-01

Reformulating constitutive relation in terms of gradient dynamics (being derivative of a dissipation potential) brings additional information on stability, metastability and instability of the dynamics with respect to perturbations of the constitutive relation, called CR-stability. CR-instability is connected to the loss of convexity of the dissipation potential, which makes the Legendre-conjugate dissipation potential multivalued and causes dissipative phase transitions that are not induced by non-convexity of free energy, but by non-convexity of the dissipation potential. CR-stability of the constitutive relation with respect to perturbations is then manifested by constructing evolution equations for the perturbations in a thermodynamically sound way (CR-extension). As a result, interesting experimental observations of behavior of complex fluids under shear flow and supercritical boiling curve can be explained.

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.

On the convexity of ROC curves estimated from radiological test results

PubMed Central

Pesce, Lorenzo L.; Metz, Charles E.; Berbaum, Kevin S.

2010-01-01

Rationale and Objectives Although an ideal observer’s receiver operating characteristic (ROC) curve must be convex — i.e., its slope must decrease monotonically — published fits to empirical data often display “hooks.” Such fits sometimes are accepted on the basis of an argument that experiments are done with real, rather than ideal, observers. However, the fact that ideal observers must produce convex curves does not imply that convex curves describe only ideal observers. This paper aims to identify the practical implications of non-convex ROC curves and the conditions that can lead to empirical and/or fitted ROC curves that are not convex. Materials and Methods This paper views non-convex ROC curves from historical, theoretical and statistical perspectives, which we describe briefly. We then consider population ROC curves with various shapes and analyze the types of medical decisions that they imply. Finally, we describe how sampling variability and curve-fitting algorithms can produce ROC curve estimates that include hooks. Results We show that hooks in population ROC curves imply the use of an irrational decision strategy, even when the curve doesn’t cross the chance line, and therefore usually are untenable in medical settings. Moreover, we sketch a simple approach to improve any non-convex ROC curve by adding statistical variation to the decision process. Finally, we sketch how to test whether hooks present in ROC data are likely to have been caused by chance alone and how some hooked ROCs found in the literature can be easily explained as fitting artifacts or modeling issues. Conclusion In general, ROC curve fits that show hooks should be looked upon with suspicion unless other arguments justify their presence. PMID:20599155

Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

NASA Astrophysics Data System (ADS)

Chen, Wei

2015-07-01

In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

Integer Partitions and Convexity

NASA Astrophysics Data System (ADS)

Bouroubi, Sadek

2007-06-01

Let n be an integer >=1, and let p(n,k) and P(n,k) count the number of partitions of n into k parts, and the number of partitions of n into parts less than or equal to k, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdos.

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

A novel comprehensive learning artificial bee colony optimizer for dynamic optimization biological problems.

PubMed

Su, Weixing; Chen, Hanning; Liu, Fang; Lin, Na; Jing, Shikai; Liang, Xiaodan; Liu, Wei

2017-03-01

There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC) for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell's pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.

Dikin-type algorithms for dextrous grasping force optimization

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

Buss, M.; Faybusovich, L.; Moore, J.B.

1998-08-01

One of the central issues in dextrous robotic hand grasping is to balance external forces acting on the object and at the same time achieve grasp stability and minimum grasping effort. A companion paper shows that the nonlinear friction-force limit constraints on grasping forces are equivalent to the positive definiteness of a certain matrix subject to linear constraints. Further, compensation of the external object force is also a linear constraint on this matrix. Consequently, the task of grasping force optimization can be formulated as a problem with semidefinite constraints. In this paper, two versions of strictly convex cost functions, onemore » of them self-concordant, are considered. These are twice-continuously differentiable functions that tend to infinity at the boundary of possible definiteness. For the general class of such cost functions, Dikin-type algorithms are presented. It is shown that the proposed algorithms guarantee convergence to the unique solution of the semidefinite programming problem associated with dextrous grasping force optimization. Numerical examples demonstrate the simplicity of implementation, the good numerical properties, and the optimality of the approach.« less

Exact solution for the optimal neuronal layout problem.

PubMed

Chklovskii, Dmitri B

2004-10-01

Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.

Bicriteria Network Optimization Problem using Priority-based Genetic Algorithm

NASA Astrophysics Data System (ADS)

Gen, Mitsuo; Lin, Lin; Cheng, Runwei

Network optimization is being an increasingly important and fundamental issue in the fields such as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. In many applications, however, there are several criteria associated with traversing each edge of a network. For example, cost and flow measures are both important in the networks. As a result, there has been recent interest in solving Bicriteria Network Optimization Problem. The Bicriteria Network Optimization Problem is known a NP-hard. The efficient set of paths may be very large, possibly exponential in size. Thus the computational effort required to solve it can increase exponentially with the problem size in the worst case. In this paper, we propose a genetic algorithm (GA) approach used a priority-based chromosome for solving the bicriteria network optimization problem including maximum flow (MXF) model and minimum cost flow (MCF) model. The objective is to find the set of Pareto optimal solutions that give possible maximum flow with minimum cost. This paper also combines Adaptive Weight Approach (AWA) that utilizes some useful information from the current population to readjust weights for obtaining a search pressure toward a positive ideal point. Computer simulations show the several numerical experiments by using some difficult-to-solve network design problems, and show the effectiveness of the proposed method.

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

Optimal rail container shipment planning problem in multimodal transportation

NASA Astrophysics Data System (ADS)

Cao, Chengxuan; Gao, Ziyou; Li, Keping

2012-09-01

The optimal rail container shipment planning problem in multimodal transportation is studied in this article. The characteristics of the multi-period planning problem is presented and the problem is formulated as a large-scale 0-1 integer programming model, which maximizes the total profit generated by all freight bookings accepted in a multi-period planning horizon subject to the limited capacities. Two heuristic algorithms are proposed to obtain an approximate optimal solution of the problem. Finally, numerical experiments are conducted to demonstrate the proposed formulation and heuristic algorithms.

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.

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

An algorithm for the split-feasibility problems with application to the split-equality problem.

PubMed

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

NASA Astrophysics Data System (ADS)

Vasant, Pandian

2011-06-01

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

Convex formulation of multiple instance learning from positive and unlabeled bags.

PubMed

Bao, Han; Sakai, Tomoya; Sato, Issei; Sugiyama, Masashi

2018-05-24

Multiple instance learning (MIL) is a variation of traditional supervised learning problems where data (referred to as bags) are composed of sub-elements (referred to as instances) and only bag labels are available. MIL has a variety of applications such as content-based image retrieval, text categorization, and medical diagnosis. Most of the previous work for MIL assume that training bags are fully labeled. However, it is often difficult to obtain an enough number of labeled bags in practical situations, while many unlabeled bags are available. A learning framework called PU classification (positive and unlabeled classification) can address this problem. In this paper, we propose a convex PU classification method to solve an MIL problem. We experimentally show that the proposed method achieves better performance with significantly lower computation costs than an existing method for PU-MIL. Copyright © 2018 Elsevier Ltd. All rights reserved.

Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems

NASA Technical Reports Server (NTRS)

Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.

2000-01-01

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.

An angular biasing method using arbitrary convex polyhedra for Monte Carlo radiation transport calculations

DOE PAGES

Kulesza, Joel A.; Solomon, Clell J.; Kiedrowski, Brian C.

2018-01-02

This paper presents a new method for performing angular biasing in Monte Carlo radiation transport codes using arbitrary convex polyhedra to define regions of interest toward which to project particles (DXTRAN regions). The method is derived and is implemented using axis-aligned right parallelepipeds (AARPPs) and arbitrary convex polyhedra. Attention is also paid to possible numerical complications and areas for future refinement. A series of test problems are executed with void, purely absorbing, purely scattering, and 50% absorbing/50% scattering materials. For all test problems tally results using AARPP and polyhedral DXTRAN regions agree with analog and/or spherical DXTRAN results within statisticalmore » uncertainties. In cases with significant scattering the figure of merit (FOM) using AARPP or polyhedral DXTRAN regions is lower than with spherical regions despite the ability to closely fit the tally region. This is because spherical DXTRAN processing is computationally less expensive than AARPP or polyhedral DXTRAN processing. Thus, it is recommended that the speed of spherical regions be considered versus the ability to closely fit the tally region with an AARPP or arbitrary polyhedral region. It is also recommended that short calculations be made prior to final calculations to compare the FOM for the various DXTRAN geometries because of the influence of the scattering behavior.« less

A novel metaheuristic for continuous optimization problems: Virus optimization algorithm

NASA Astrophysics Data System (ADS)

Liang, Yun-Chia; Rodolfo Cuevas Juarez, Josue

2016-01-01

A novel metaheuristic for continuous optimization problems, named the virus optimization algorithm (VOA), is introduced and investigated. VOA is an iteratively population-based method that imitates the behaviour of viruses attacking a living cell. The number of viruses grows at each replication and is controlled by an immune system (a so-called 'antivirus') to prevent the explosive growth of the virus population. The viruses are divided into two classes (strong and common) to balance the exploitation and exploration effects. The performance of the VOA is validated through a set of eight benchmark functions, which are also subject to rotation and shifting effects to test its robustness. Extensive comparisons were conducted with over 40 well-known metaheuristic algorithms and their variations, such as artificial bee colony, artificial immune system, differential evolution, evolutionary programming, evolutionary strategy, genetic algorithm, harmony search, invasive weed optimization, memetic algorithm, particle swarm optimization and simulated annealing. The results showed that the VOA is a viable solution for continuous optimization.

Worst case estimation of homology design by convex analysis

NASA Technical Reports Server (NTRS)

Yoshikawa, N.; Elishakoff, Isaac; Nakagiri, S.

1998-01-01

The methodology of homology design is investigated for optimum design of advanced structures. for which the achievement of delicate tasks by the aid of active control system is demanded. The proposed formulation of homology design, based on the finite element sensitivity analysis, necessarily requires the specification of external loadings. The formulation to evaluate the worst case for homology design caused by uncertain fluctuation of loadings is presented by means of the convex model of uncertainty, in which uncertainty variables are assigned to discretized nodal forces and are confined within a conceivable convex hull given as a hyperellipse. The worst case of the distortion from objective homologous deformation is estimated by the Lagrange multiplier method searching the point to maximize the error index on the boundary of the convex hull. The validity of the proposed method is demonstrated in a numerical example using the eleven-bar truss structure.

Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem

NASA Astrophysics Data System (ADS)

Rahmalia, Dinita

2017-08-01

Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

PubMed

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION

PubMed Central

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

2016-01-01

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method—named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)—for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results. PMID:26778864

Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints

NASA Astrophysics Data System (ADS)

Kmet', Tibor; Kmet'ová, Mária

2009-09-01

A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

Evaluating the effects of real power losses in optimal power flow based storage integration

DOE PAGES

Castillo, Anya; Gayme, Dennice

2017-03-27

This study proposes a DC optimal power flow (DCOPF) with losses formulation (the `-DCOPF+S problem) and uses it to investigate the role of real power losses in OPF based grid-scale storage integration. We derive the `- DCOPF+S problem by augmenting a standard DCOPF with storage (DCOPF+S) problem to include quadratic real power loss approximations. This procedure leads to a multi-period nonconvex quadratically constrained quadratic program, which we prove can be solved to optimality using either a semidefinite or second order cone relaxation. Our approach has some important benefits over existing models. It is more computationally tractable than ACOPF with storagemore » (ACOPF+S) formulations and the provably exact convex relaxations guarantee that an optimal solution can be attained for a feasible problem. Adding loss approximations to a DCOPF+S model leads to a more accurate representation of locational marginal prices, which have been shown to be critical to determining optimal storage dispatch and siting in prior ACOPF+S based studies. Case studies demonstrate the improved accuracy of the `-DCOPF+S model over a DCOPF+S model and the computational advantages over an ACOPF+S formulation.« less

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

The solution of private problems for optimization heat exchangers parameters

NASA Astrophysics Data System (ADS)

Melekhin, A.

2017-11-01

The relevance of the topic due to the decision of problems of the economy of resources in heating systems of buildings. To solve this problem we have developed an integrated method of research which allows solving tasks on optimization of parameters of heat exchangers. This method decides multicriteria optimization problem with the program nonlinear optimization on the basis of software with the introduction of an array of temperatures obtained using thermography. The author have developed a mathematical model of process of heat exchange in heat exchange surfaces of apparatuses with the solution of multicriteria optimization problem and check its adequacy to the experimental stand in the visualization of thermal fields, an optimal range of managed parameters influencing the process of heat exchange with minimal metal consumption and the maximum heat output fin heat exchanger, the regularities of heat exchange process with getting generalizing dependencies distribution of temperature on the heat-release surface of the heat exchanger vehicles, defined convergence of the results of research in the calculation on the basis of theoretical dependencies and solving mathematical model.

Design optimization of transmitting antennas for weakly coupled magnetic induction communication systems

PubMed Central

2017-01-01

This work focuses on the design of transmitting coils in weakly coupled magnetic induction communication systems. We propose several optimization methods that reduce the active, reactive and apparent power consumption of the coil. These problems are formulated as minimization problems, in which the power consumed by the transmitting coil is minimized, under the constraint of providing a required magnetic field at the receiver location. We develop efficient numeric and analytic methods to solve the resulting problems, which are of high dimension, and in certain cases non-convex. For the objective of minimal reactive power an analytic solution for the optimal current distribution in flat disc transmitting coils is provided. This problem is extended to general three-dimensional coils, for which we develop an expression for the optimal current distribution. Considering the objective of minimal apparent power, a method is developed to reduce the computational complexity of the problem by transforming it to an equivalent problem of lower dimension, allowing a quick and accurate numeric solution. These results are verified experimentally by testing a number of coil geometries. The results obtained allow reduced power consumption and increased performances in magnetic induction communication systems. Specifically, for wideband systems, an optimal design of the transmitter coil reduces the peak instantaneous power provided by the transmitter circuitry, and thus reduces its size, complexity and cost. PMID:28192463

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.

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

Social interaction as a heuristic for combinatorial optimization problems

NASA Astrophysics Data System (ADS)

Fontanari, José F.

2010-11-01

We investigate the performance of a variant of Axelrod’s model for dissemination of culture—the Adaptive Culture Heuristic (ACH)—on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents’ strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N1/4 so that the number of agents must increase with the fourth power of the problem size, N∝F4 , to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F6 which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

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

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.

Reducing the duality gap in partially convex programming

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

Correa, R.

1994-12-31

We consider the non-linear minimization program {alpha} = min{sub z{element_of}D, x{element_of}C}{l_brace}f{sub 0}(z, x) : f{sub i}(z, x) {<=} 0, i {element_of} {l_brace}1, ..., m{r_brace}{r_brace} where f{sub i}(z, {center_dot}) are convex functions, C is convex and D is compact. Following Ben-Tal, Eiger and Gershowitz we prove the existence of a partial dual program whose optimum is arbitrarily close to {alpha}. The idea, corresponds to the branching principle in Branch and Bound methods. We describe such a kind of algorithm for obtaining the desired partial dual.

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.

Discrete-time entropy formulation of optimal and adaptive control problems

NASA Technical Reports Server (NTRS)

Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.

1992-01-01

The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.

Convex Arrhenius plots and their interpretation

PubMed Central

Truhlar, Donald G.; Kohen, Amnon

2001-01-01

This paper draws attention to selected experiments on enzyme-catalyzed reactions that show convex Arrhenius plots, which are very rare, and points out that Tolman's interpretation of the activation energy places a fundamental model-independent constraint on any detailed explanation of these reactions. The analysis presented here shows that in such systems, the rate coefficient as a function of energy is not just increasing more slowly than expected, it is actually decreasing. This interpretation of the data provides a constraint on proposed microscopic models, i.e., it requires that any successful model of a reaction with a convex Arrhenius plot should be consistent with the microcanonical rate coefficient being a decreasing function of energy. The implications and limitations of this analysis to interpreting enzyme mechanisms are discussed. This model-independent conclusion has broad applicability to all fields of kinetics, and we also draw attention to an analogy with diffusion in metastable fluids and glasses. PMID:11158559

Application of tabu search to deterministic and stochastic optimization problems

NASA Astrophysics Data System (ADS)

Gurtuna, Ozgur

During the past two decades, advances in computer science and operations research have resulted in many new optimization methods for tackling complex decision-making problems. One such method, tabu search, forms the basis of this thesis. Tabu search is a very versatile optimization heuristic that can be used for solving many different types of optimization problems. Another research area, real options, has also gained considerable momentum during the last two decades. Real options analysis is emerging as a robust and powerful method for tackling decision-making problems under uncertainty. Although the theoretical foundations of real options are well-established and significant progress has been made in the theory side, applications are lagging behind. A strong emphasis on practical applications and a multidisciplinary approach form the basic rationale of this thesis. The fundamental concepts and ideas behind tabu search and real options are investigated in order to provide a concise overview of the theory supporting both of these two fields. This theoretical overview feeds into the design and development of algorithms that are used to solve three different problems. The first problem examined is a deterministic one: finding the optimal servicing tours that minimize energy and/or duration of missions for servicing satellites around Earth's orbit. Due to the nature of the space environment, this problem is modeled as a time-dependent, moving-target optimization problem. Two solution methods are developed: an exhaustive method for smaller problem instances, and a method based on tabu search for larger ones. The second and third problems are related to decision-making under uncertainty. In the second problem, tabu search and real options are investigated together within the context of a stochastic optimization problem: option valuation. By merging tabu search and Monte Carlo simulation, a new method for studying options, Tabu Search Monte Carlo (TSMC) method, is

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

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

Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

2015-09-01

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

Preconditioning 2D Integer Data for Fast Convex Hull Computations

PubMed Central

2016-01-01

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved. PMID:26938221

Preconditioning 2D Integer Data for Fast Convex Hull Computations.

PubMed

Cadenas, José Oswaldo; Megson, Graham M; Luengo Hendriks, Cris L

2016-01-01

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

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

Optimal network modification for spectral radius dependent phase transitions

NASA Astrophysics Data System (ADS)

Rosen, Yonatan; Kirsch, Lior; Louzoun, Yoram

2016-09-01

The dynamics of contact processes on networks is often determined by the spectral radius of the networks adjacency matrices. A decrease of the spectral radius can prevent the outbreak of an epidemic, or impact the synchronization among systems of coupled oscillators. The spectral radius is thus tightly linked to network dynamics and function. As such, finding the minimal change in network structure necessary to reach the intended spectral radius is important theoretically and practically. Given contemporary big data resources such as large scale communication or social networks, this problem should be solved with a low runtime complexity. We introduce a novel method for the minimal decrease in weights of edges required to reach a given spectral radius. The problem is formulated as a convex optimization problem, where a global optimum is guaranteed. The method can be easily adjusted to an efficient discrete removal of edges. We introduce a variant of the method which finds optimal decrease with a focus on weights of vertices. The proposed algorithm is exceptionally scalable, solving the problem for real networks of tens of millions of edges in a short time.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Solving optimization problems by the public goods game

NASA Astrophysics Data System (ADS)

Javarone, Marco Alberto

2017-09-01

We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities. The proposed method considers a population whose agents are provided with a random solution to the given problem. In doing so, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. Notably, agents with better solutions provide higher contributions, while those with lower ones tend to imitate the solution of richer agents for increasing their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization problems, our work aims to highlight the potentiality of evolutionary game theory beyond its current horizons.

A coherent Ising machine for 2000-node optimization problems

NASA Astrophysics Data System (ADS)

Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

2016-11-01

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Convexity of level lines of Martin functions and applications

NASA Astrophysics Data System (ADS)

Gallagher, A.-K.; Lebl, J.; Ramachandran, K.

2018-01-01

Let Ω be an unbounded domain in R× Rd. A positive harmonic function u on Ω that vanishes on the boundary of Ω is called a Martin function. In this note, we show that, when Ω is convex, the superlevel sets of a Martin function are also convex. As a consequence we obtain that if in addition Ω has certain symmetry with respect to the t-axis, and partial Ω is sufficiently flat, then the maximum of any Martin function along a slice Ω \\cap ({t}× R^d) is attained at (t, 0).

Fundamental differences between optimization code test problems in engineering applications

NASA Technical Reports Server (NTRS)

Eason, E. D.

1984-01-01

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

Topology optimization of unsteady flow problems using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Nørgaard, Sebastian; Sigmund, Ole; Lazarov, Boyan

2016-02-01

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

The Sizing and Optimization Language, (SOL): Computer language for design problems

NASA Technical Reports Server (NTRS)

Lucas, Stephen H.; Scotti, Stephen J.

1988-01-01

The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

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.

Ordinal optimization and its application to complex deterministic problems

NASA Astrophysics Data System (ADS)

Yang, Mike Shang-Yu

1998-10-01

We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through numerical means, but the burden of high complexities remains to tax the simulation with an exorbitant computing cost for each evaluation. Such a resource requirement makes local fine-tuning of a known design difficult under most circumstances, let alone global optimization. Kolmogorov equivalence of complexity and randomness in computation theory is introduced to resolve this difficulty by converting the complex deterministic model to a stochastic pseudo-model composed of a simple deterministic component and a white-noise like stochastic term. The resulting randomness is then dealt with by a noise-robust approach called Ordinal Optimization. Ordinal Optimization utilizes Goal Softening and Ordinal Comparison to achieve an efficient and quantifiable selection of designs in the initial search process. The approach is substantiated by a case study in the turbine blade manufacturing process. The problem involves the optimization of the manufacturing process of the integrally bladed rotor in the turbine engines of U.S. Air Force fighter jets. The intertwining interactions among the material, thermomechanical, and geometrical changes makes the current FEM approach prohibitively uneconomical in the optimization process. The generalized OO approach to complex deterministic problems is applied here with great success. Empirical results indicate a saving of nearly 95% in the computing cost.

Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm

NASA Astrophysics Data System (ADS)

Kania, Adhe; Sidarto, Kuntjoro Adji

2016-02-01

Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.

Effective Teaching of Economics: A Constrained Optimization Problem?

ERIC Educational Resources Information Center

Hultberg, Patrik T.; Calonge, David Santandreu

2017-01-01

One of the fundamental tenets of economics is that decisions are often the result of optimization problems subject to resource constraints. Consumers optimize utility, subject to constraints imposed by prices and income. As economics faculty, instructors attempt to maximize student learning while being constrained by their own and students'…

Automatic segmentation for brain MR images via a convex optimized segmentation and bias field correction coupled model.

PubMed

Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui

2014-09-01

Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results. Copyright © 2014 Elsevier Inc. All rights reserved.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem.

PubMed

Rajeswari, M; Amudhavel, J; Pothula, Sujatha; Dhavachelvan, P

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem

PubMed Central

Amudhavel, J.; Pothula, Sujatha; Dhavachelvan, P.

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria. PMID:28473849

The Role of Intuition in the Solving of Optimization Problems

ERIC Educational Resources Information Center

Malaspina, Uldarico; Font, Vicenc

2010-01-01

This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

Improving multi-objective reservoir operation optimization with sensitivity-informed problem decomposition

NASA Astrophysics Data System (ADS)

Chu, J. G.; Zhang, C.; Fu, G. T.; Li, Y.; Zhou, H. C.

2015-04-01

This study investigates the effectiveness of a sensitivity-informed method for multi-objective operation of reservoir systems, which uses global sensitivity analysis as a screening tool to reduce the computational demands. Sobol's method is used to screen insensitive decision variables and guide the formulation of the optimization problems with a significantly reduced number of decision variables. This sensitivity-informed problem decomposition dramatically reduces the computational demands required for attaining high quality approximations of optimal tradeoff relationships between conflicting design objectives. The search results obtained from the reduced complexity multi-objective reservoir operation problems are then used to pre-condition the full search of the original optimization problem. In two case studies, the Dahuofang reservoir and the inter-basin multi-reservoir system in Liaoning province, China, sensitivity analysis results show that reservoir performance is strongly controlled by a small proportion of decision variables. Sensitivity-informed problem decomposition and pre-conditioning are evaluated in their ability to improve the efficiency and effectiveness of multi-objective evolutionary optimization. Overall, this study illustrates the efficiency and effectiveness of the sensitivity-informed method and the use of global sensitivity analysis to inform problem decomposition when solving the complex multi-objective reservoir operation problems.

Sub-problem Optimization With Regression and Neural Network Approximators

NASA Technical Reports Server (NTRS)

Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.

2003-01-01

Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.

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

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

Another convex combination of product states for the separable Werner state

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

Azuma, Hiroo; Ban, Masashi; CREST, Japan Science and Technology Agency, 1-1-9 Yaesu, Chuo-ku, Tokyo 103-0028

2006-03-15

In this paper, we write down the separable Werner state in a two-qubit system explicitly as a convex combination of product states, which is different from the convex combination obtained by Wootters' method. The Werner state in a two-qubit system has a single real parameter and varies from inseparable to separable according to the value of its parameter. We derive a hidden variable model that is induced by our decomposed form for the separable Werner state. From our explicit form of the convex combination of product states, we understand the following: The critical point of the parameter for separability ofmore » the Werner state comes from positivity of local density operators of the qubits.« less

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.

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.

New Convex and Spherical Structures of Bare Boron Clusters

NASA Astrophysics Data System (ADS)

Boustani, Ihsan

1997-10-01

New stable structures of bare boron clusters can easily be obtained and constructed with the help of an "Aufbau Principle" suggested by a systematicab initioHF-SCF and direct CI study. It is concluded that boron cluster formation can be established by elemental units of pentagonal and hexagonal pyramids. New convex and small spherical clusters different from the classical known forms of boron crystal structures are obtained by a combination of both basic units. Convex structures simulate boron surfaces which can be considered as segments of open or closed spheres. Both convex clusters B16and B46have energies close to those of their conjugate quasi-planar clusters, which are relatively stable and can be considered to act as a calibration mark. The closed spherical clusters B12, B22, B32, and B42are less stable than the corresponding conjugated quasi-planar structures. As a consequence, highly stable spherical boron clusters can systematically be predicted when their conjugate quasi-planar clusters are determined and energies are compared.

Optimal pre-scheduling of problem remappings

NASA Technical Reports Server (NTRS)

Nicol, David M.; Saltz, Joel H.

1987-01-01

A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.

An optimized algorithm for multiscale wideband deconvolution of radio astronomical images

NASA Astrophysics Data System (ADS)

Offringa, A. R.; Smirnov, O.

2017-10-01

We describe a new multiscale deconvolution algorithm that can also be used in a multifrequency mode. The algorithm only affects the minor clean loop. In single-frequency mode, the minor loop of our improved multiscale algorithm is over an order of magnitude faster than the casa multiscale algorithm, and produces results of similar quality. For multifrequency deconvolution, a technique named joined-channel cleaning is used. In this mode, the minor loop of our algorithm is two to three orders of magnitude faster than casa msmfs. We extend the multiscale mode with automated scale-dependent masking, which allows structures to be cleaned below the noise. We describe a new scale-bias function for use in multiscale cleaning. We test a second deconvolution method that is a variant of the moresane deconvolution technique, and uses a convex optimization technique with isotropic undecimated wavelets as dictionary. On simple well-calibrated data, the convex optimization algorithm produces visually more representative models. On complex or imperfect data, the convex optimization algorithm has stability issues.

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.

Redundant interferometric calibration as a complex optimization problem

NASA Astrophysics Data System (ADS)

Grobler, T. L.; Bernardi, G.; Kenyon, J. S.; Parsons, A. R.; Smirnov, O. M.

2018-05-01

Observations of the redshifted 21 cm line from the epoch of reionization have recently motivated the construction of low-frequency radio arrays with highly redundant configurations. These configurations provide an alternative calibration strategy - `redundant calibration' - and boost sensitivity on specific spatial scales. In this paper, we formulate calibration of redundant interferometric arrays as a complex optimization problem. We solve this optimization problem via the Levenberg-Marquardt algorithm. This calibration approach is more robust to initial conditions than current algorithms and, by leveraging an approximate matrix inversion, allows for further optimization and an efficient implementation (`redundant STEFCAL'). We also investigated using the preconditioned conjugate gradient method as an alternative to the approximate matrix inverse, but found that its computational performance is not competitive with respect to `redundant STEFCAL'. The efficient implementation of this new algorithm is made publicly available.

Ant colony optimization for solving university facility layout problem

NASA Astrophysics Data System (ADS)

Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

2013-04-01

Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

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.

Optimization-based additive decomposition of weakly coercive problems with applications

DOE PAGES

Bochev, Pavel B.; Ridzal, Denis

2016-01-27

In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem,more » our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.« less

On Several Fundamental Problems of Optimization, Estimation, and Scheduling in Wireless Communications

NASA Astrophysics Data System (ADS)

Gao, Qian

For both the conventional radio frequency and the comparably recent optical wireless communication systems, extensive effort from the academia had been made in improving the network spectrum efficiency and/or reducing the error rate. To achieve these goals, many fundamental challenges such as power efficient constellation design, nonlinear distortion mitigation, channel training design, network scheduling and etc. need to be properly addressed. In this dissertation, novel schemes are proposed accordingly to deal with specific problems falling in category of these challenges. Rigorous proofs and analyses are provided for each of our work to make a fair comparison with the corresponding peer works to clearly demonstrate the advantages. The first part of this dissertation considers a multi-carrier optical wireless system employing intensity modulation (IM) and direct detection (DD). A block-wise constellation design is presented, which treats the DC-bias that conventionally used solely for biasing purpose as an information basis. Our scheme, we term it MSM-JDCM, takes advantage of the compactness of sphere packing in a higher dimensional space, and in turn power efficient constellations are obtained by solving an advanced convex optimization problem. Besides the significant power gains, the MSM-JDCM has many other merits such as being capable of mitigating nonlinear distortion by including a peak-to-power ratio (PAPR) constraint, minimizing inter-symbol-interference (ISI) caused by frequency-selective fading with a novel precoder designed and embedded, and further reducing the bit-error-rate (BER) by combining with an optimized labeling scheme. The second part addresses several optimization problems in a multi-color visible light communication system, including power efficient constellation design, joint pre-equalizer and constellation design, and modeling of different structured channels with cross-talks. Our novel constellation design scheme, termed CSK-Advanced, is

Quantum algorithm for energy matching in hard optimization problems

NASA Astrophysics Data System (ADS)

Baldwin, C. L.; Laumann, C. R.

2018-06-01

We consider the ability of local quantum dynamics to solve the "energy-matching" problem: given an instance of a classical optimization problem and a low-energy state, find another macroscopically distinct low-energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here, we show that the introduction of quantum dynamics can provide a speedup over classical algorithms in a large class of hard optimization problems. Tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. Specifically, we study energy matching in the random p -spin model of spin-glass theory. Using perturbation theory and exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field "trapped" phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field "excited" phase, in which the field excites the system into high-energy states, effectively forgetting the initial energy; and (3) the intermediate "tunneling" phase, in which the system succeeds at energy matching. The rate at which distant states are found in the tunneling phase, although exponentially slow in system size, is exponentially faster than classical search algorithms.

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.

Proposal of Evolutionary Simplex Method for Global Optimization Problem

NASA Astrophysics Data System (ADS)

Shimizu, Yoshiaki

To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.

Issues and Strategies in Solving Multidisciplinary Optimization Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya

2013-01-01

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the

Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications

DTIC Science & Technology

2015-06-24

WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Arizona State University School of Mathematical & Statistical Sciences 901 S...SUPPLEMENTARY NOTES 14. ABSTRACT The major goals of this project were completed: the exact solution of previously unsolved challenging combinatorial optimization... combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly

Harmony search algorithm: application to the redundancy optimization problem

NASA Astrophysics Data System (ADS)

Nahas, Nabil; Thien-My, Dao

2010-09-01

The redundancy optimization problem is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system performance, given different system-level constraints. This article presents an efficient algorithm based on the harmony search algorithm (HSA) to solve this optimization problem. The HSA is a new nature-inspired algorithm which mimics the improvization process of music players. Two kinds of problems are considered in testing the proposed algorithm, with the first limited to the binary series-parallel system, where the problem consists of a selection of elements and redundancy levels used to maximize the system reliability given various system-level constraints; the second problem for its part concerns the multi-state series-parallel systems with performance levels ranging from perfect operation to complete failure, and in which identical redundant elements are included in order to achieve a desirable level of availability. Numerical results for test problems from previous research are reported and compared. The results of HSA showed that this algorithm could provide very good solutions when compared to those obtained through other approaches.

Noah, Joseph and Convex Hulls

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chau, Y.; Chapman, S. C.

2010-12-01

The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].

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.

Guided particle swarm optimization method to solve general nonlinear optimization problems

NASA Astrophysics Data System (ADS)

Abdelhalim, Alyaa; Nakata, Kazuhide; El-Alem, Mahmoud; Eltawil, Amr

2018-04-01

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder-Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.

Quadratic Optimization in the Problems of Active Control of Sound

NASA Technical Reports Server (NTRS)

Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Two hybrid compaction algorithms for the layout optimization problem.

PubMed

Xiao, Ren-Bin; Xu, Yi-Chun; Amos, Martyn

2007-01-01

In this paper we present two new algorithms for the layout optimization problem: this concerns the placement of circular, weighted objects inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of the container. This problem carries real practical significance in industrial applications (such as the design of satellites), as well as being of significant theoretical interest. We present two nature-inspired algorithms for this problem, the first based on simulated annealing, and the second on particle swarm optimization. We compare our algorithms with the existing best-known algorithm, and show that our approaches out-perform it in terms of both solution quality and execution time.

Optimal Control Problems with Switching Points. Ph.D. Thesis, 1990 Final Report

NASA Technical Reports Server (NTRS)

Seywald, Hans

1991-01-01

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Direct SQP-methods for solving optimal control problems with delays

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

Goellmann, L.; Bueskens, C.; Maurer, H.

The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method formore » retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.« less

Multiresolution strategies for the numerical solution of optimal control problems

NASA Astrophysics Data System (ADS)

Jain, Sachin

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a

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.

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

PubMed Central

Naeem, Muhammad; Illanko, Kandasamy; Karmokar, Ashok; Anpalagan, Alagan; Jaseemuddin, Muhammad

2013-01-01

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated. PMID:23966194

Iterating the Number of Intersection Points of the Diagonals of Irregular Convex Polygons, or C (n, 4) the Hard Way!

ERIC Educational Resources Information Center

Hathout, Leith

2007-01-01

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

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

The baker’s map with a convex hole

NASA Astrophysics Data System (ADS)

Clark, Lyndsey; Hare, Kevin G.; Sidorov, Nikita

2018-07-01

We consider the baker’s map B on the unit square X and an open convex set which we regard as a hole. The survivor set is defined as the set of all points in X whose B-trajectories are disjoint from H. The main purpose of this paper is to study holes H for which (dimension traps) as well as those for which any periodic trajectory of B intersects (cycle traps). We show that any H which lies in the interior of X is not a dimension trap. This means that, unlike the doubling map and other one-dimensional examples, we can have for H whose Lebesgue measure is arbitrarily close to one. Also, we describe holes which are dimension or cycle traps, critical in the sense that if we consider a strictly convex subset, then the corresponding property in question no longer holds. We also determine such that for all convex H whose Lebesgue measure is less than δ. This paper may be seen as a first extension of our work begun in Clark (2016 Discrete Continuous Dyn. Syst. A 6 1249–69 Clark 2016 PhD Dissertation The University of Manchester; Glendinning and Sidorov 2015 Ergod. Theor. Dynam. Syst. 35 1208–28 Hare and Sidorov 2014 Mon.hefte Math. 175 347–65 Sidorov 2014 Acta Math. Hung. 143 298–312) to higher dimensions.

Measurement system for diffraction efficiency of convex gratings

NASA Astrophysics Data System (ADS)

Liu, Peng; Chen, Xin-hua; Zhou, Jian-kang; Zhao, Zhi-cheng; Liu, Quan; Luo, Chao; Wang, Xiao-feng; Tang, Min-xue; Shen, Wei-min

2017-08-01

A measurement system for diffraction efficiency of convex gratings is designed. The measurement system mainly includes four components as a light source, a front system, a dispersing system that contains a convex grating, and a detector. Based on the definition and measuring principle of diffraction efficiency, the optical scheme of the measurement system is analyzed and the design result is given. Then, in order to validate the feasibility of the designed system, the measurement system is set up and the diffraction efficiency of a convex grating with the aperture of 35 mm, the curvature-radius of 72mm, the blazed angle of 6.4°, the grating period of 2.5μm and the working waveband of 400nm-900nm is tested. Based on GUM (Guide to the Expression of Uncertainty in Measurement), the uncertainties in the measuring results are evaluated. The measured diffraction efficiency data are compared to the theoretical ones, which are calculated based on the grating groove parameters got by an atomic force microscope and Rigorous Couple Wave Analysis, and the reliability of the measurement system is illustrated. Finally, the measurement performance of the system is analyzed and tested. The results show that, the testing accuracy, the testing stability and the testing repeatability are 2.5%, 0.085% and 3.5% , respectively.

Optimization in First Semester Calculus: A Look at a Classic Problem

ERIC Educational Resources Information Center

LaRue, Renee; Infante, Nicole Engelke

2015-01-01

Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…

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

HSTLBO: A hybrid algorithm based on Harmony Search and Teaching-Learning-Based Optimization for complex high-dimensional optimization problems.

PubMed

Tuo, Shouheng; Yong, Longquan; Deng, Fang'an; Li, Yanhai; Lin, Yong; Lu, Qiuju

2017-01-01

Harmony Search (HS) and Teaching-Learning-Based Optimization (TLBO) as new swarm intelligent optimization algorithms have received much attention in recent years. Both of them have shown outstanding performance for solving NP-Hard optimization problems. However, they also suffer dramatic performance degradation for some complex high-dimensional optimization problems. Through a lot of experiments, we find that the HS and TLBO have strong complementarity each other. The HS has strong global exploration power but low convergence speed. Reversely, the TLBO has much fast convergence speed but it is easily trapped into local search. In this work, we propose a hybrid search algorithm named HSTLBO that merges the two algorithms together for synergistically solving complex optimization problems using a self-adaptive selection strategy. In the HSTLBO, both HS and TLBO are modified with the aim of balancing the global exploration and exploitation abilities, where the HS aims mainly to explore the unknown regions and the TLBO aims to rapidly exploit high-precision solutions in the known regions. Our experimental results demonstrate better performance and faster speed than five state-of-the-art HS variants and show better exploration power than five good TLBO variants with similar run time, which illustrates that our method is promising in solving complex high-dimensional optimization problems. The experiment on portfolio optimization problems also demonstrate that the HSTLBO is effective in solving complex read-world application.

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.

Optimizing conjunctive use of surface water and groundwater resources with stochastic dynamic programming

NASA Astrophysics Data System (ADS)

Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Rosbjerg, Dan; Bauer-Gottwein, Peter

2014-05-01

Optimal management of conjunctive use of surface water and groundwater has been attempted with different algorithms in the literature. In this study, a hydro-economic modelling approach to optimize conjunctive use of scarce surface water and groundwater resources under uncertainty is presented. A stochastic dynamic programming (SDP) approach is used to minimize the basin-wide total costs arising from water allocations and water curtailments. Dynamic allocation problems with inclusion of groundwater resources proved to be more complex to solve with SDP than pure surface water allocation problems due to head-dependent pumping costs. These dynamic pumping costs strongly affect the total costs and can lead to non-convexity of the future cost function. The water user groups (agriculture, industry, domestic) are characterized by inelastic demands and fixed water allocation and water supply curtailment costs. As in traditional SDP approaches, one step-ahead sub-problems are solved to find the optimal management at any time knowing the inflow scenario and reservoir/aquifer storage levels. These non-linear sub-problems are solved using a genetic algorithm (GA) that minimizes the sum of the immediate and future costs for given surface water reservoir and groundwater aquifer end storages. The immediate cost is found by solving a simple linear allocation sub-problem, and the future costs are assessed by interpolation in the total cost matrix from the following time step. Total costs for all stages, reservoir states, and inflow scenarios are used as future costs to drive a forward moving simulation under uncertain water availability. The use of a GA to solve the sub-problems is computationally more costly than a traditional SDP approach with linearly interpolated future costs. However, in a two-reservoir system the future cost function would have to be represented by a set of planes, and strict convexity in both the surface water and groundwater dimension cannot be maintained

Optimal Planning and Problem-Solving

NASA Technical Reports Server (NTRS)

Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg

2008-01-01

CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

LP and NLP decomposition without a master problem

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

Fuller, D.; Lan, B.

We describe a new algorithm for decomposition of linear programs and a class of convex nonlinear programs, together with theoretical properties and some test results. Its most striking feature is the absence of a master problem; the subproblems pass primal and dual proposals directly to one another. The algorithm is defined for multi-stage LPs or NLPs, in which the constraints link the current stage`s variables to earlier stages` variables. This problem class is general enough to include many problem structures that do not immediately suggest stages, such as block diagonal problems. The basic algorithmis derived for two-stage problems and extendedmore » to more than two stages through nested decomposition. The main theoretical result assures convergence, to within any preset tolerance of the optimal value, in a finite number of iterations. This asymptotic convergence result contrasts with the results of limited tests on LPs, in which the optimal solution is apparently found exactly, i.e., to machine accuracy, in a small number of iterations. The tests further suggest that for LPs, the new algorithm is faster than the simplex method applied to the whole problem, as long as the stages are linked loosely; that the speedup over the simpex method improves as the number of stages increases; and that the algorithm is more reliable than nested Dantzig-Wolfe or Benders` methods in its improvement over the simplex method.« less

Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm

NASA Astrophysics Data System (ADS)

Ausaf, Muhammad Farhan; Gao, Liang; Li, Xinyu

2015-12-01

For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.