Linear Matrix Inequality Method for a Quadratic Performance Index Minimization Problem with a class of Bilinear Matrix Inequality Conditions

NASA Astrophysics Data System (ADS)

Tanemura, M.; Chida, Y.

2016-09-01

There are a lot of design problems of control system which are expressed as a performance index minimization under BMI conditions. However, a minimization problem expressed as LMIs can be easily solved because of the convex property of LMIs. Therefore, many researchers have been studying transforming a variety of control design problems into convex minimization problems expressed as LMIs. This paper proposes an LMI method for a quadratic performance index minimization problem with a class of BMI conditions. The minimization problem treated in this paper includes design problems of state-feedback gain for switched system and so on. The effectiveness of the proposed method is verified through a state-feedback gain design for switched systems and a numerical simulation using the designed feedback gains.

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.

Development of Analysis Tools for Certification of Flight Control Laws

DTIC Science & Technology

2009-03-31

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

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

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

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

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

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

NASA Astrophysics Data System (ADS)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Optimal Link Removal for Epidemic Mitigation: A Two-Way Partitioning Approach

PubMed Central

Enns, Eva A.; Mounzer, Jeffrey J.; Brandeau, Margaret L.

2011-01-01

The structure of the contact network through which a disease spreads may influence the optimal use of resources for epidemic control. In this work, we explore how to minimize the spread of infection via quarantining with limited resources. In particular, we examine which links should be removed from the contact network, given a constraint on the number of removable links, such that the number of nodes which are no longer at risk for infection is maximized. We show how this problem can be posed as a non-convex quadratically constrained quadratic program (QCQP), and we use this formulation to derive a link removal algorithm. The performance of our QCQP-based algorithm is validated on small Erdős-Renyi and small-world random graphs, and then tested on larger, more realistic networks, including a real-world network of injection drug use. We show that our approach achieves near optimal performance and out-perform so ther intuitive link removal algorithms, such as removing links in order of edge centrality. PMID:22115862

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.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

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

PubMed

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

2018-03-01

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

Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

PubMed

Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham

2017-11-01

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.

Nonconvex model predictive control for commercial refrigeration

NASA Astrophysics Data System (ADS)

Gybel Hovgaard, Tobias; Boyd, Stephen; Larsen, Lars F. S.; Bagterp Jørgensen, John

2013-08-01

We consider the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor, and is used to cool multiple areas or rooms. In each time period we choose cooling capacity to each unit and a common evaporation temperature. The goal is to minimise the total energy cost, using real-time electricity prices, while obeying temperature constraints on the zones. We propose a variation on model predictive control to achieve this goal. When the right variables are used, the dynamics of the system are linear, and the constraints are convex. The cost function, however, is nonconvex due to the temperature dependence of thermodynamic efficiency. To handle this nonconvexity we propose a sequential convex optimisation method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real time. We demonstrate our method on a realistic model, with a full year simulation and 15-minute time periods, using historical electricity prices and weather data, as well as random variations in thermal load. These simulations show substantial cost savings, on the order of 30%, compared to a standard thermostat-based control system. Perhaps more important, we see that the method exhibits sophisticated response to real-time variations in electricity prices. This demand response is critical to help balance real-time uncertainties in generation capacity associated with large penetration of intermittent renewable energy sources in a future smart grid.

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

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

A Path Algorithm for Constrained Estimation

PubMed Central

Zhou, Hua; Lange, Kenneth

2013-01-01

Many least-square problems involve affine equality and inequality constraints. Although there are a variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current article proposes a new path-following algorithm for quadratic programming that replaces hard constraints by what are called exact penalties. Similar penalties arise in l1 regularization in model selection. In the regularization setting, penalties encapsulate prior knowledge, and penalized parameter estimates represent a trade-off between the observed data and the prior knowledge. Classical penalty methods of optimization, such as the quadratic penalty method, 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. The exact path-following method 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. Path following in Lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the Lasso and generalized Lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well-chosen examples illustrate the mechanics and potential of path following. This article has supplementary materials available online. PMID:24039382

Fast Algorithms for Designing Unimodular Waveform(s) With Good Correlation Properties

NASA Astrophysics Data System (ADS)

Li, Yongzhe; Vorobyov, Sergiy A.

2018-03-01

In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding optimization problems can quickly grow to large scale with increasing the code length and number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are non-convex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as non-convex quartic optimization problems in frequency domain, and then simplify them into quadratic problems by utilizing the majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or non-convex optimization problems. While designing our fast algorithms, we find out and use inherent algebraic structures in the objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form which allows to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

The spectral positioning algorithm of new spectrum vehicle based on convex programming in wireless sensor network

NASA Astrophysics Data System (ADS)

Zhang, Yongjun; Lu, Zhixin

2017-10-01

Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.

2000-01-01

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

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Local classifier weighting by quadratic programming.

PubMed

Cevikalp, Hakan; Polikar, Robi

2008-10-01

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

A trust region-based approach to optimize triple response systems

NASA Astrophysics Data System (ADS)

Fan, Shu-Kai S.; Fan, Chihhao; Huang, Chia-Fen

2014-05-01

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke-Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.

Global stability of plane Couette flow beyond the energy stability limit

NASA Astrophysics Data System (ADS)

Fuentes, Federico; Goluskin, David

2017-11-01

This talk will present computations verifying that the laminar state of plane Couette flow is nonlinearly stable to all perturbations. The Reynolds numbers up to which this globally stability is verified are larger than those at which stability can be proven by the energy method, which is the typical method for demonstrating nonlinear stability of a fluid flow. This improvement is achieved by constructing Lyapunov functions that are more general than the energy. These functions are not restricted to being quadratic, and they are allowed to depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal choice of such a Lyapunov function is a convex optimization problem, and it can be constructed with computer assistance by solving a semidefinite program. This general method will be described in a companion talk by David Goluskin; the present talk focuses on its application to plane Couette flow.

Simulation of superconducting tapes and coils with convex quadratic programming method

NASA Astrophysics Data System (ADS)

Zhang, Yan; Song, Yuntao; Wang, Lei; Liu, Xufeng

2015-08-01

Second-generation (2G) high-temperature superconducting coated conductors are playing an increasingly important role in power applications due to their large current density under high magnetic fields. In this paper, we conclude and explore the ability and possible potential of J formulation from the mathematical modeling point of view. An equivalent matrix form of J formulation has been presented and a relation between electromagnetic quantities and Karush-Kuhn-Tucker (KKT) conditions in optimization theory has been discovered. The use of the latest formulae to calculate inductance in a coil system and the primal-dual interior-point method algorithm is a trial to make the process of modeling stylized and build a bridge to commercial optimization solvers. Two different dependences of the critical current density on the magnetic field have been used in order to make a comparison with those published papers.

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

Identification of spatially-localized initial conditions via sparse PCA

NASA Astrophysics Data System (ADS)

Dwivedi, Anubhav; Jovanovic, Mihailo

2017-11-01

Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. This work was supported by Office of Naval Research through Grant Number N00014-15-1-2522.

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

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

PubMed

Liang, X B; Wang, J

2000-01-01

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

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.

Half-quadratic variational regularization methods for speckle-suppression and edge-enhancement in SAR complex image

NASA Astrophysics Data System (ADS)

Zhao, Xia; Wang, Guang-xin

2008-12-01

Synthetic aperture radar (SAR) is an active remote sensing sensor. It is a coherent imaging system, the speckle is its inherent default, which affects badly the interpretation and recognition of the SAR targets. Conventional methods of removing the speckle is studied usually in real SAR image, which reduce the edges of the images at the same time as depressing the speckle. Morever, Conventional methods lost the information about images phase. Removing the speckle and enhancing the target and edge simultaneously are still a puzzle. To suppress the spckle and enhance the targets and the edges simultaneously, a half-quadratic variational regularization method in complex SAR image is presented, which is based on the prior knowledge of the targets and the edge. Due to the non-quadratic and non- convex quality and the complexity of the cost function, a half-quadratic variational regularization variation is used to construct a new cost function,which is solved by alternate optimization. In the proposed scheme, the construction of the model, the solution of the model and the selection of the model peremeters are studied carefully. In the end, we validate the method using the real SAR data.Theoretic analysis and the experimental results illustrate the the feasibility of the proposed method. Further more, the proposed method can preserve the information about images phase.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Data-Driven Engineering of Social Dynamics: Pattern Matching and Profit Maximization

PubMed Central

Peng, Huan-Kai; Lee, Hao-Chih; Pan, Jia-Yu; Marculescu, Radu

2016-01-01

In this paper, we define a new problem related to social media, namely, the data-driven engineering of social dynamics. More precisely, given a set of observations from the past, we aim at finding the best short-term intervention that can lead to predefined long-term outcomes. Toward this end, we propose a general formulation that covers two useful engineering tasks as special cases, namely, pattern matching and profit maximization. By incorporating a deep learning model, we derive a solution using convex relaxation and quadratic-programming transformation. Moreover, we propose a data-driven evaluation method in place of the expensive field experiments. Using a Twitter dataset, we demonstrate the effectiveness of our dynamics engineering approach for both pattern matching and profit maximization, and study the multifaceted interplay among several important factors of dynamics engineering, such as solution validity, pattern-matching accuracy, and intervention cost. Finally, the method we propose is general enough to work with multi-dimensional time series, so it can potentially be used in many other applications. PMID:26771830

Vehicle trajectory linearisation to enable efficient optimisation of the constant speed racing line

NASA Astrophysics Data System (ADS)

Timings, Julian P.; Cole, David J.

2012-06-01

A driver model is presented capable of optimising the trajectory of a simple dynamic nonlinear vehicle, at constant forward speed, so that progression along a predefined track is maximised as a function of time. In doing so, the model is able to continually operate a vehicle at its lateral-handling limit, maximising vehicle performance. The technique used forms a part of the solution to the motor racing objective of minimising lap time. A new approach of formulating the minimum lap time problem is motivated by the need for a more computationally efficient and robust tool-set for understanding on-the-limit driving behaviour. This has been achieved through set point-dependent linearisation of the vehicle model and coupling the vehicle-track system using an intrinsic coordinate description. Through this, the geometric vehicle trajectory had been linearised relative to the track reference, leading to new path optimisation algorithm which can be formed as a computationally efficient convex quadratic programming problem.

Data-Driven Engineering of Social Dynamics: Pattern Matching and Profit Maximization.

PubMed

Peng, Huan-Kai; Lee, Hao-Chih; Pan, Jia-Yu; Marculescu, Radu

2016-01-01

In this paper, we define a new problem related to social media, namely, the data-driven engineering of social dynamics. More precisely, given a set of observations from the past, we aim at finding the best short-term intervention that can lead to predefined long-term outcomes. Toward this end, we propose a general formulation that covers two useful engineering tasks as special cases, namely, pattern matching and profit maximization. By incorporating a deep learning model, we derive a solution using convex relaxation and quadratic-programming transformation. Moreover, we propose a data-driven evaluation method in place of the expensive field experiments. Using a Twitter dataset, we demonstrate the effectiveness of our dynamics engineering approach for both pattern matching and profit maximization, and study the multifaceted interplay among several important factors of dynamics engineering, such as solution validity, pattern-matching accuracy, and intervention cost. Finally, the method we propose is general enough to work with multi-dimensional time series, so it can potentially be used in many other applications.

Robust Group Sparse Beamforming for Multicast Green Cloud-RAN With Imperfect CSI

NASA Astrophysics Data System (ADS)

Shi, Yuanming; Zhang, Jun; Letaief, Khaled B.

2015-09-01

In this paper, we investigate the network power minimization problem for the multicast cloud radio access network (Cloud-RAN) with imperfect channel state information (CSI). The key observation is that network power minimization can be achieved by adaptively selecting active remote radio heads (RRHs) via controlling the group-sparsity structure of the beamforming vector. However, this yields a non-convex combinatorial optimization problem, for which we propose a three-stage robust group sparse beamforming algorithm. In the first stage, a quadratic variational formulation of the weighted mixed l1/l2-norm is proposed to induce the group-sparsity structure in the aggregated beamforming vector, which indicates those RRHs that can be switched off. A perturbed alternating optimization algorithm is then proposed to solve the resultant non-convex group-sparsity inducing optimization problem by exploiting its convex substructures. In the second stage, we propose a PhaseLift technique based algorithm to solve the feasibility problem with a given active RRH set, which helps determine the active RRHs. Finally, the semidefinite relaxation (SDR) technique is adopted to determine the robust multicast beamformers. Simulation results will demonstrate the convergence of the perturbed alternating optimization algorithm, as well as, the effectiveness of the proposed algorithm to minimize the network power consumption for multicast Cloud-RAN.

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

PubMed

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

2012-10-21

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

Comparison of optimization algorithms in intensity-modulated radiation therapy planning

NASA Astrophysics Data System (ADS)

Kendrick, Rachel

Intensity-modulated radiation therapy is used to better conform the radiation dose to the target, which includes avoiding healthy tissue. Planning programs employ optimization methods to search for the best fluence of each photon beam, and therefore to create the best treatment plan. The Computational Environment for Radiotherapy Research (CERR), a program written in MATLAB, was used to examine some commonly-used algorithms for one 5-beam plan. Algorithms include the genetic algorithm, quadratic programming, pattern search, constrained nonlinear optimization, simulated annealing, the optimization method used in Varian EclipseTM, and some hybrids of these. Quadratic programing, simulated annealing, and a quadratic/simulated annealing hybrid were also separately compared using different prescription doses. The results of each dose-volume histogram as well as the visual dose color wash were used to compare the plans. CERR's built-in quadratic programming provided the best overall plan, but avoidance of the organ-at-risk was rivaled by other programs. Hybrids of quadratic programming with some of these algorithms seems to suggest the possibility of better planning programs, as shown by the improved quadratic/simulated annealing plan when compared to the simulated annealing algorithm alone. Further experimentation will be done to improve cost functions and computational time.

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.

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

Multimodal Image Alignment via Linear Mapping between Feature Modalities.

PubMed

Jiang, Yanyun; Zheng, Yuanjie; Hou, Sujuan; Chang, Yuchou; Gee, James

2017-01-01

We propose a novel landmark matching based method for aligning multimodal images, which is accomplished uniquely by resolving a linear mapping between different feature modalities. This linear mapping results in a new measurement on similarity of images captured from different modalities. In addition, our method simultaneously solves this linear mapping and the landmark correspondences by minimizing a convex quadratic function. Our method can estimate complex image relationship between different modalities and nonlinear nonrigid spatial transformations even in the presence of heavy noise, as shown in our experiments carried out by using a variety of image modalities.

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.

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

PubMed

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

2013-01-01

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

The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers

NASA Astrophysics Data System (ADS)

Neff, Patrizio; Lankeit, Johannes; Ghiba, Ionel-Dumitrel; Martin, Robert; Steigmann, David

2015-08-01

We consider a family of isotropic volumetric-isochoric decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U, where μ > 0 is the infinitesimal shear modulus, is the infinitesimal bulk modulus with the first Lamé constant, are dimensionless parameters, is the gradient of deformation, is the right stretch tensor and is the deviatoric part (the projection onto the traceless tensors) of the strain tensor log U. For small elastic strains, the energies reduce to first order to the classical quadratic Hencky energy which is known to be not rank-one convex. The main result in this paper is that in plane elastostatics the energies of the family are polyconvex for , extending a previous finding on its rank-one convexity. Our method uses a judicious application of Steigmann's polyconvexity criteria based on the representation of the energy in terms of the principal invariants of the stretch tensor U. These energies also satisfy suitable growth and coercivity conditions. We formulate the equilibrium equations, and we prove the existence of minimizers by the direct methods of the calculus of variations.

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.

Quadratic Programming for Allocating Control Effort

NASA Technical Reports Server (NTRS)

Singh, Gurkirpal

2005-01-01

A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

Seven Wonders of the Ancient and Modern Quadratic World.

ERIC Educational Resources Information Center

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

Robust decentralized power system controller design: Integrated approach

NASA Astrophysics Data System (ADS)

Veselý, Vojtech

2017-09-01

A unique approach to the design of gain scheduled controller (GSC) is presented. The proposed design procedure is based on the Bellman-Lyapunov equation, guaranteed cost and robust stability conditions using the parameter dependent quadratic stability approach. The obtained feasible design procedures for robust GSC design are in the form of BMI with guaranteed convex stability conditions. The obtained design results and their properties are illustrated in the simultaneously design of controllers for simple model (6-order) turbogenerator. The results of the obtained design procedure are a PI automatic voltage regulator (AVR) for synchronous generator, a PI governor controller and a power system stabilizer for excitation system.

SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

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

Ungun, B; Stanford University School of Medicine, Stanford, CA; Fu, A

2016-06-15

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction,more » we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.« less

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.

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

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

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 .

Magnetic MIMO Signal Processing and Optimization for Wireless Power Transfer

NASA Astrophysics Data System (ADS)

Yang, Gang; Moghadam, Mohammad R. Vedady; Zhang, Rui

2017-06-01

In magnetic resonant coupling (MRC) enabled multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems, multiple transmitters (TXs) each with one single coil are used to enhance the efficiency of simultaneous power transfer to multiple single-coil receivers (RXs) by constructively combining their induced magnetic fields at the RXs, a technique termed "magnetic beamforming". In this paper, we study the optimal magnetic beamforming design in a multi-user MIMO MRC-WPT system. We introduce the multi-user power region that constitutes all the achievable power tuples for all RXs, subject to the given total power constraint over all TXs as well as their individual peak voltage and current constraints. We characterize each boundary point of the power region by maximizing the sum-power deliverable to all RXs subject to their minimum harvested power constraints. For the special case without the TX peak voltage and current constraints, we derive the optimal TX current allocation for the single-RX setup in closed-form as well as that for the multi-RX setup. In general, the problem is a non-convex quadratically constrained quadratic programming (QCQP), which is difficult to solve. For the case of one single RX, we show that the semidefinite relaxation (SDR) of the problem is tight. For the general case with multiple RXs, based on SDR we obtain two approximate solutions by applying time-sharing and randomization, respectively. Moreover, for practical implementation of magnetic beamforming, we propose a novel signal processing method to estimate the magnetic MIMO channel due to the mutual inductances between TXs and RXs. Numerical results show that our proposed magnetic channel estimation and adaptive beamforming schemes are practically effective, and can significantly improve the power transfer efficiency and multi-user performance trade-off in MIMO MRC-WPT systems.

On Using Homogeneous Polynomials To Design Anisotropic Yield Functions With Tension/Compression Symmetry/Assymetry

NASA Astrophysics Data System (ADS)

Soare, S.; Yoon, J. W.; Cazacu, O.

2007-05-01

With few exceptions, non-quadratic homogeneous polynomials have received little attention as possible candidates for yield functions. One reason might be that not every such polynomial is a convex function. In this paper we show that homogeneous polynomials can be used to develop powerful anisotropic yield criteria, and that imposing simple constraints on the identification process leads, aposteriori, to the desired convexity property. It is shown that combinations of such polynomials allow for modeling yielding properties of metallic materials with any crystal structure, i.e. both cubic and hexagonal which display strength differential effects. Extensions of the proposed criteria to 3D stress states are also presented. We apply these criteria to the description of the aluminum alloy AA2090T3. We prove that a sixth order orthotropic homogeneous polynomial is capable of a satisfactory description of this alloy. Next, applications to the deep drawing of a cylindrical cup are presented. The newly proposed criteria were implemented as UMAT subroutines into the commercial FE code ABAQUS. We were able to predict six ears on the AA2090T3 cup's profile. Finally, we show that a tension/compression asymmetry in yielding can have an important effect on the earing profile.

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.

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

An exact general remeshing scheme applied to physically conservative voxelization

DOE PAGES

Powell, Devon; Abel, Tom

2015-05-21

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal themore » corresponding integral over the output mesh. We refer to this as “physically conservative voxelization.” At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara [48], who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.« less

Regression model, artificial neural network, and cost estimation for biosorption of Ni(II)-ions from aqueous solutions by Potamogeton pectinatus.

PubMed

Fawzy, Manal; Nasr, Mahmoud; Adel, Samar; Helmi, Shacker

2018-03-21

This study investigated the application of Potamogeton pectinatus for Ni(II)-ions biosorption from aqueous solutions. FTIR spectra showed that the functional groups of -OH, C-H, -C = O, and -COO- could form an organometallic complex with Ni(II)-ions on the biomaterial surface. SEM/EDX analysis indicated that the voids on the biosorbent surface were blocked due to Ni(II)-ions uptake via an ion exchange mechanism. For Ni(II)-ions of 50 mg/L, the adsorption efficiency recorded 63.4% at pH: 5, biosorbent dosage: 10 g/L, and particle-diameter: 0.125-0.25 mm within 180 minutes. A quadratic model depicted that the plot of removal efficiency against pH or contact time caused quadratic-linear concave up curves, whereas the curve of initial Ni(II)-ions was quadratic-linear convex down. Artificial neural network with a structure of 5 - 6 - 1 was able to predict the adsorption efficiency (R 2 : 0.967). The relative importance of inputs was: initial Ni(II)-ions > pH > contact time > biosorbent dosage > particle-size. Freundlich isotherm described well the adsorption mechanism (R 2 : 0.974), which indicated a multilayer adsorption onto energetically heterogeneous surfaces. The net cost of using P. pectinatus for the removal of Ni(II)-ions (4.25 ± 1.26 mg/L) from real industrial effluents within 30 minutes was 3.4 $USD/m 3 .

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.

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

ERIC Educational Resources Information Center

Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

2015-01-01

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP). GMAC® Research Report RR-14-01

ERIC Educational Resources Information Center

Han, Kyung T.; Rudner, Lawrence M.

2014-01-01

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…

Manpower Targets and Educational Investments

ERIC Educational Resources Information Center

Ritzen, Jo M.

1976-01-01

Discusses the use of quadratic programming to calculate the optimal distribution of educational investments required to closely approach manpower targets when financial resources are insufficient to meet manpower targets completely. Demonstrates use of the quadratic programming approach by applying it to the training of supervisory technicians in…

Consensus for multi-agent systems with time-varying input delays

NASA Astrophysics Data System (ADS)

Yuan, Chengzhi; Wu, Fen

2017-10-01

This paper addresses the consensus control problem for linear multi-agent systems subject to uniform time-varying input delays and external disturbance. A novel state-feedback consensus protocol is proposed under the integral quadratic constraint (IQC) framework, which utilises not only the relative state information from neighbouring agents but also the real-time information of delays by means of the dynamic IQC system states for feedback control. Based on this new consensus protocol, the associated IQC-based control synthesis conditions are established and fully characterised as linear matrix inequalities (LMIs), such that the consensus control solution with optimal ? disturbance attenuation performance can be synthesised efficiently via convex optimisation. A numerical example is used to demonstrate the proposed approach.

Extremal entanglement witnesses

NASA Astrophysics Data System (ADS)

Hansen, Leif Ove; Hauge, Andreas; Myrheim, Jan; Sollid, Per Øyvind

2015-02-01

We present a study of extremal entanglement witnesses on a bipartite composite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus TrΩρ≥0 when Ω is a witness and ρ is a pure product state, ρ=ψψ† with ψ=ϕ⊗χ. The set of witnesses of unit trace is a compact convex set, uniquely defined by its extremal points. The expectation value f(ϕ,χ)=TrΩρ as a function of vectors ϕ and χ is a positive semidefinite biquadratic form. Every zero of f(ϕ,χ) imposes strong real-linear constraints on f and Ω. The real and symmetric Hessian matrix at the zero must be positive semidefinite. Its eigenvectors with zero eigenvalue, if such exist, we call Hessian zeros. A zero of f(ϕ,χ) is quadratic if it has no Hessian zeros, otherwise it is quartic. We call a witness quadratic if it has only quadratic zeros, and quartic if it has at least one quartic zero. A main result we prove is that a witness is extremal if and only if no other witness has the same, or a larger, set of zeros and Hessian zeros. A quadratic extremal witness has a minimum number of isolated zeros depending on dimensions. If a witness is not extremal, then the constraints defined by its zeros and Hessian zeros determine all directions in which we may search for witnesses having more zeros or Hessian zeros. A finite number of iterated searches in random directions, by numerical methods, leads to an extremal witness which is nearly always quadratic and has the minimum number of zeros. We discuss briefly some topics related to extremal witnesses, in particular the relation between the facial structures of the dual sets of witnesses and separable states. We discuss the relation between extremality and optimality of witnesses, and a conjecture of separability of the so-called structural physical approximation (SPA) of an optimal witness. Finally, we discuss how to treat the entanglement witnesses on a complex Hilbert space as a subset of the witnesses on a real Hilbert space.

A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming.

PubMed

Liu, Jing; Duan, Yongrui; Sun, Min

2017-01-01

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval [Formula: see text]. Under the conditions that the objective function is convex and the solution set is nonempty, we establish the convergence results of the proposed method, including the global convergence, the worst-case [Formula: see text] convergence rate in both the ergodic and the non-ergodic senses, where k denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method.

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

NASA Astrophysics Data System (ADS)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

On Using Homogeneous Polynomials To Design Anisotropic Yield Functions With Tension/Compression Symmetry/Assymetry

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

Soare, S.; Cazacu, O.; Yoon, J. W.

With few exceptions, non-quadratic homogeneous polynomials have received little attention as possible candidates for yield functions. One reason might be that not every such polynomial is a convex function. In this paper we show that homogeneous polynomials can be used to develop powerful anisotropic yield criteria, and that imposing simple constraints on the identification process leads, aposteriori, to the desired convexity property. It is shown that combinations of such polynomials allow for modeling yielding properties of metallic materials with any crystal structure, i.e. both cubic and hexagonal which display strength differential effects. Extensions of the proposed criteria to 3D stressmore » states are also presented. We apply these criteria to the description of the aluminum alloy AA2090T3. We prove that a sixth order orthotropic homogeneous polynomial is capable of a satisfactory description of this alloy. Next, applications to the deep drawing of a cylindrical cup are presented. The newly proposed criteria were implemented as UMAT subroutines into the commercial FE code ABAQUS. We were able to predict six ears on the AA2090T3 cup's profile. Finally, we show that a tension/compression asymmetry in yielding can have an important effect on the earing profile.« less

An efficient self-organizing map designed by genetic algorithms for the traveling salesman problem.

PubMed

Jin, Hui-Dong; Leung, Kwong-Sak; Wong, Man-Leung; Xu, Z B

2003-01-01

As a typical combinatorial optimization problem, the traveling salesman problem (TSP) has attracted extensive research interest. In this paper, we develop a self-organizing map (SOM) with a novel learning rule. It is called the integrated SOM (ISOM) since its learning rule integrates the three learning mechanisms in the SOM literature. Within a single learning step, the excited neuron is first dragged toward the input city, then pushed to the convex hull of the TSP, and finally drawn toward the middle point of its two neighboring neurons. A genetic algorithm is successfully specified to determine the elaborate coordination among the three learning mechanisms as well as the suitable parameter setting. The evolved ISOM (eISOM) is examined on three sets of TSP to demonstrate its power and efficiency. The computation complexity of the eISOM is quadratic, which is comparable to other SOM-like neural networks. Moreover, the eISOM can generate more accurate solutions than several typical approaches for TSP including the SOM developed by Budinich, the expanding SOM, the convex elastic net, and the FLEXMAP algorithm. Though its solution accuracy is not yet comparable to some sophisticated heuristics, the eISOM is one of the most accurate neural networks for the TSP.

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Linkages between Snow Cover Seasonality, Terrain, and Land Surface Phenology in the Highland Pastures of Kyrgyzstan

NASA Astrophysics Data System (ADS)

Henebry, Geoffrey; Tomaszewska, Monika; Kelgenbaeva, Kamilya

2017-04-01

In the highlands of Kyrgyzstan, vertical transhumance is the foundation of montane agropastoralism. Terrain attributes, such as elevation, slope, and aspect, affect snow cover seasonality, which is a key influence on the timing of plant growth and forage availability. Our study areas include the highland pastures in Central Tien Shan mountains, specifically in the rayons of Naryn and At-Bashy in Naryn oblast, and Alay and Chong-Alay rayons in Osh oblast. To explore the linkages between snow cover seasonality and land surface phenology as modulated by terrain and variations in thermal time, we use 16 years (2001-2016) of Landsat surface reflectance data at 30 m resolution with MODIS land surface temperature and snow cover products at 1 km and 500 m resolution, respectively, and two digital elevation models, SRTM and ASTER GDEM. We model snow cover seasonality using frost degree-days and land surface phenology using growing degree-days as quadratic functions of thermal time: a convex quadratic (CxQ) model for land surface phenology and a concave quadratic (CvQ) model for snow cover seasonality. From the fitted parameter coefficients, we calculated phenometrics, including "peak height" and "thermal time to peak" for the CxQ models and "trough depth" and "thermal time to trough" for the CvQ models. We explore how these phenometrics change as a function of elevation and slope-aspect interactions and due to interannual variability. Further, we examine how snow cover duration and timing affects the subsequent peak height and thermal time to peak in wetter, drier, and normal years.

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.

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.

A computational study of the use of an optimization-based method for simulating large multibody systems.

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

Petra, C.; Gavrea, B.; Anitescu, M.

2009-01-01

The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of Lemke-type algorithms and solvers such as the PATH solver proved to be robust. However, for large systems, the PATH solver or any other pivotal algorithm becomes unpractical from a computational point of view. The convex relaxation proposed by one of the authors allows the formulation of the integration step as a QPD, for whichmore » a wide variety of state-of-the-art solvers are available. In what follows we report the results obtained solving that subproblem when using the QP solvers MOSEK, OOQP, TRON, and BLMVM. OOQP is presented with both the symmetric indefinite solver MA27 and our Cholesky reformulation using the CHOLMOD package. We investigate computational performance and address the correctness of the results from a modeling point of view. We conclude that the OOQP solver, particularly with the CHOLMOD linear algebra solver, has predictable performance and memory use patterns and is far more competitive for these problems than are the other solvers.« less

PSQP: Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

A linear programming manual

NASA Technical Reports Server (NTRS)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

An accelerated proximal augmented Lagrangian method and its application in compressive sensing.

PubMed

Sun, Min; Liu, Jing

2017-01-01

As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case [Formula: see text] convergence rate of PALM-IPR in a non-ergodic sense. Finally, numerical results show that our new method is feasible and efficient for solving compressive sensing.

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

Zhang, Xiaohu; Shi, Di; Wang, Zhiwei

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

Quantitative Homogenization in Nonlinear Elasticity for Small Loads

NASA Astrophysics Data System (ADS)

Neukamm, Stefan; Schäffner, Mathias

2018-04-01

We study quantitative periodic homogenization of integral functionals in the context of nonlinear elasticity. Under suitable assumptions on the energy densities (in particular frame indifference; minimality, non-degeneracy and smoothness at the identity; {p ≥q d} -growth from below; and regularity of the microstructure), we show that in a neighborhood of the set of rotations, the multi-cell homogenization formula of non-convex homogenization reduces to a single-cell formula. The latter can be expressed with the help of correctors. We prove that the homogenized integrand admits a quadratic Taylor expansion in an open neighborhood of the rotations - a result that can be interpreted as the fact that homogenization and linearization commute close to the rotations. Moreover, for small applied loads, we provide an estimate on the homogenization error in terms of a quantitative two-scale expansion.

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

Cooperative Solutions in Multi-Person Quadratic Decision Problems: Finite-Horizon and State-Feedback Cost-Cumulant Control Paradigm

DTIC Science & Technology

2007-01-01

CONTRACT NUMBER Problems: Finite -Horizon and State-Feedback Cost-Cumulant Control Paradigm (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...cooperative cost-cumulant control regime for the class of multi-person single-objective decision problems characterized by quadratic random costs and... finite -horizon integral quadratic cost associated with a linear stochastic system . Since this problem formation is parameterized by the number of cost

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

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

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

SNS programming environment user's guide

NASA Technical Reports Server (NTRS)

Tennille, Geoffrey M.; Howser, Lona M.; Humes, D. Creig; Cronin, Catherine K.; Bowen, John T.; Drozdowski, Joseph M.; Utley, Judith A.; Flynn, Theresa M.; Austin, Brenda A.

1992-01-01

The computing environment is briefly described for the Supercomputing Network Subsystem (SNS) of the Central Scientific Computing Complex of NASA Langley. The major SNS computers are a CRAY-2, a CRAY Y-MP, a CONVEX C-210, and a CONVEX C-220. The software is described that is common to all of these computers, including: the UNIX operating system, computer graphics, networking utilities, mass storage, and mathematical libraries. Also described is file management, validation, SNS configuration, documentation, and customer services.

Drawing road networks with focus regions.

PubMed

Haunert, Jan-Henrik; Sering, Leon

2011-12-01

Mobile users of maps typically need detailed information about their surroundings plus some context information about remote places. In order to avoid that the map partly gets too dense, cartographers have designed mapping functions that enlarge a user-defined focus region--such functions are sometimes called fish-eye projections. The extra map space occupied by the enlarged focus region is compensated by distorting other parts of the map. We argue that, in a map showing a network of roads relevant to the user, distortion should preferably take place in those areas where the network is sparse. Therefore, we do not apply a predefined mapping function. Instead, we consider the road network as a graph whose edges are the road segments. We compute a new spatial mapping with a graph-based optimization approach, minimizing the square sum of distortions at edges. Our optimization method is based on a convex quadratic program (CQP); CQPs can be solved in polynomial time. Important requirements on the output map are expressed as linear inequalities. In particular, we show how to forbid edge crossings. We have implemented our method in a prototype tool. For instances of different sizes, our method generated output maps that were far less distorted than those generated with a predefined fish-eye projection. Future work is needed to automate the selection of roads relevant to the user. Furthermore, we aim at fast heuristics for application in real-time systems. © 2011 IEEE

Support vector machines for nuclear reactor state estimation

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

Zavaljevski, N.; Gross, K. C.

2000-02-14

Validation of nuclear power reactor signals is often performed by comparing signal prototypes with the actual reactor signals. The signal prototypes are often computed based on empirical data. The implementation of an estimation algorithm which can make predictions on limited data is an important issue. A new machine learning algorithm called support vector machines (SVMS) recently developed by Vladimir Vapnik and his coworkers enables a high level of generalization with finite high-dimensional data. The improved generalization in comparison with standard methods like neural networks is due mainly to the following characteristics of the method. The input data space is transformedmore » into a high-dimensional feature space using a kernel function, and the learning problem is formulated as a convex quadratic programming problem with a unique solution. In this paper the authors have applied the SVM method for data-based state estimation in nuclear power reactors. In particular, they implemented and tested kernels developed at Argonne National Laboratory for the Multivariate State Estimation Technique (MSET), a nonlinear, nonparametric estimation technique with a wide range of applications in nuclear reactors. The methodology has been applied to three data sets from experimental and commercial nuclear power reactor applications. The results are promising. The combination of MSET kernels with the SVM method has better noise reduction and generalization properties than the standard MSET algorithm.« less

The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface

NASA Astrophysics Data System (ADS)

Klass, E. V.

2017-12-01

The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.

Optimization by nonhierarchical asynchronous decomposition

NASA Technical Reports Server (NTRS)

Shankar, Jayashree; Ribbens, Calvin J.; Haftka, Raphael T.; Watson, Layne T.

1992-01-01

Large scale optimization problems are tractable only if they are somehow decomposed. Hierarchical decompositions are inappropriate for some types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategy for nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two dimensional quadratic programs. The algorithm is carefully analyzed for quadratic programs, and a number of modifications are suggested to improve its robustness.

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.

Duality in non-linear programming

NASA Astrophysics Data System (ADS)

Jeyalakshmi, K.

2018-04-01

In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.

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.

Distance majorization and its applications.

PubMed

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

2014-08-01

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

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

Using Land Surface Phenology to Detect Land Use Change in the Northern Great Plains

NASA Astrophysics Data System (ADS)

Nguyen, L. H.; Henebry, G. M.

2017-12-01

The Northern Great Plains of the US have been undergoing many types of land cover / land use change over the past two decades, including expansion of irrigation, conversion of grassland to cropland, biofuels production, urbanization, and fossil fuel mining. Much of the literature on these changes has relied on post-classification change detection based on a limited number of observations per year. Here we demonstrate an approach to characterize land dynamics through land surface phenology (LSP) by synergistic use of image time series at two scales. Our study areas include regions of interest (ROIs) across the Northern Great Plains located within Landsat path overlap zones to boost the number of valid observations (free of clouds or snow) each year. We first compute accumulated growing degree-days (AGDD) from MODIS 8-day composites of land surface temperature (MOD11A2 and MYD11A2). Using Landsat Collection 1 surface reflectance-derived vegetation indices (NDVI, EVI), we then fit at each pixel a downward convex quadratic model linking the vegetation index to each year's progression of AGDD. This quadratic equation exhibits linearity in a mathematical sense; thus, the fitted models can be linearly mixed and unmixed using a set of LSP endmembers (defined by the fitted parameter coefficients of the quadratic model) that represent "pure" land cover types with distinct seasonal patterns found within the region, such as winter wheat, spring wheat, maize, soybean, sunflower, hay/pasture/grassland, developed/built-up, among others. Information about land cover corresponding to each endmember are provided by the NLCD (National Land Cover Dataset) and CDL (Cropland Data Layer). We use linear unmixing to estimate the likely proportion of each LSP endmember within particular areas stratified by latitude. By tracking the proportions over the 2001-2011 period, we can quantify various types of land transitions in the Northern Great Plains.

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.

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

Distance majorization and its applications

PubMed Central

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

2014-01-01

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

A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

NASA Astrophysics Data System (ADS)

Voloshinov, V. V.

2018-03-01

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

Minimal norm constrained interpolation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Irvine, L. D.

1985-01-01

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Improved Evolutionary Programming with Various Crossover Techniques for Optimal Power Flow Problem

NASA Astrophysics Data System (ADS)

Tangpatiphan, Kritsana; Yokoyama, Akihiko

This paper presents an Improved Evolutionary Programming (IEP) for solving the Optimal Power Flow (OPF) problem, which is considered as a non-linear, non-smooth, and multimodal optimization problem in power system operation. The total generator fuel cost is regarded as an objective function to be minimized. The proposed method is an Evolutionary Programming (EP)-based algorithm with making use of various crossover techniques, normally applied in Real Coded Genetic Algorithm (RCGA). The effectiveness of the proposed approach is investigated on the IEEE 30-bus system with three different types of fuel cost functions; namely the quadratic cost curve, the piecewise quadratic cost curve, and the quadratic cost curve superimposed by sine component. These three cost curves represent the generator fuel cost functions with a simplified model and more accurate models of a combined-cycle generating unit and a thermal unit with value-point loading effect respectively. The OPF solutions by the proposed method and Pure Evolutionary Programming (PEP) are observed and compared. The simulation results indicate that IEP requires less computing time than PEP with better solutions in some cases. Moreover, the influences of important IEP parameters on the OPF solution are described in details.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

NASA Astrophysics Data System (ADS)

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

PubMed

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example for an extreme concave case. Quadratic programming is an alternative approach for inverse planning which generates clinically satisfying plans in comparison to the clinical system and constitutes an efficient optimization process characterized by uniqueness and reproducibility of the solution.

Optimal projection method determination by Logdet Divergence and perturbed von-Neumann Divergence.

PubMed

Jiang, Hao; Ching, Wai-Ki; Qiu, Yushan; Cheng, Xiao-Qing

2017-12-14

Positive semi-definiteness is a critical property in kernel methods for Support Vector Machine (SVM) by which efficient solutions can be guaranteed through convex quadratic programming. However, a lot of similarity functions in applications do not produce positive semi-definite kernels. We propose projection method by constructing projection matrix on indefinite kernels. As a generalization of the spectrum method (denoising method and flipping method), the projection method shows better or comparable performance comparing to the corresponding indefinite kernel methods on a number of real world data sets. Under the Bregman matrix divergence theory, we can find suggested optimal λ in projection method using unconstrained optimization in kernel learning. In this paper we focus on optimal λ determination, in the pursuit of precise optimal λ determination method in unconstrained optimization framework. We developed a perturbed von-Neumann divergence to measure kernel relationships. We compared optimal λ determination with Logdet Divergence and perturbed von-Neumann Divergence, aiming at finding better λ in projection method. Results on a number of real world data sets show that projection method with optimal λ by Logdet divergence demonstrate near optimal performance. And the perturbed von-Neumann Divergence can help determine a relatively better optimal projection method. Projection method ia easy to use for dealing with indefinite kernels. And the parameter embedded in the method can be determined through unconstrained optimization under Bregman matrix divergence theory. This may provide a new way in kernel SVMs for varied objectives.

A compressed sensing based 3D resistivity inversion algorithm for hydrogeological applications

NASA Astrophysics Data System (ADS)

Ranjan, Shashi; Kambhammettu, B. V. N. P.; Peddinti, Srinivasa Rao; Adinarayana, J.

2018-04-01

Image reconstruction from discrete electrical responses pose a number of computational and mathematical challenges. Application of smoothness constrained regularized inversion from limited measurements may fail to detect resistivity anomalies and sharp interfaces separated by hydro stratigraphic units. Under favourable conditions, compressed sensing (CS) can be thought of an alternative to reconstruct the image features by finding sparse solutions to highly underdetermined linear systems. This paper deals with the development of a CS assisted, 3-D resistivity inversion algorithm for use with hydrogeologists and groundwater scientists. CS based l1-regularized least square algorithm was applied to solve the resistivity inversion problem. Sparseness in the model update vector is introduced through block oriented discrete cosine transformation, with recovery of the signal achieved through convex optimization. The equivalent quadratic program was solved using primal-dual interior point method. Applicability of the proposed algorithm was demonstrated using synthetic and field examples drawn from hydrogeology. The proposed algorithm has outperformed the conventional (smoothness constrained) least square method in recovering the model parameters with much fewer data, yet preserving the sharp resistivity fronts separated by geologic layers. Resistivity anomalies represented by discrete homogeneous blocks embedded in contrasting geologic layers were better imaged using the proposed algorithm. In comparison to conventional algorithm, CS has resulted in an efficient (an increase in R2 from 0.62 to 0.78; a decrease in RMSE from 125.14 Ω-m to 72.46 Ω-m), reliable, and fast converging (run time decreased by about 25%) solution.

Minitrack tracking function description, volume 2

NASA Technical Reports Server (NTRS)

Englar, T. S.; Mango, S. A.; Roettcher, C. A.; Watters, D. L.

1973-01-01

The minitrack tracking function is described and specific operations are identified. The subjects discussed are: (1) preprocessor listing, (2) minitrack hardware, (3) system calibration, (4) quadratic listing, and (5) quadratic flow diagram. Detailed information is provided on the construction of the tracking system and its operation. The calibration procedures are supported by mathematical models to show the application of the computer programs.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

Optomechanical design of near-null subaperture test system based on counter-rotating CGH plates

NASA Astrophysics Data System (ADS)

Li, Yepeng; Chen, Shanyong; Song, Bing; Li, Shengyi

2014-09-01

In off-axis subapertures of most convex aspheres, astigmatism and coma dominate the aberrations with approximately quadratic and linear increase as the off-axis distance increases. A pair of counter-rotating computer generated hologram (CGH) plates is proposed to generate variable amount of Zernike terms Z4 and Z6, correcting most of the astigmatism and coma for subapertures located at different positions on surfaces of various aspheric shapes. The residual subaperture aberrations are then reduced within the vertical range of measurement of the interferometer, which enables near-null test of aspheres flexibly. The alignment tolerances for the near-null optics are given with optomechanical analysis. Accordingly a novel design for mounting and aligning the CGH plates is proposed which employs three concentric rigid rings. The CGH plate is mounted in the inner ring which is supported by two couples of ball-end screws in connection with the middle ring. The CGH plate along with the inner ring is hence able to be translated in X-axis and tipped by adjusting the screws. Similarly the middle ring is able to be translated in Y-axis and tilted by another two couples of screws orthogonally arranged and connected to the outer ring. This design is featured by the large center-through hole, compact size and capability of four degrees-of-freedom alignment (lateral shift and tip-tilt). It reduces the height measured in the direction of optical axis as much as possible, which is particularly advantageous for near-null test of convex aspheres. The CGH mounts are then mounted on a pair of center-through tables realizing counter-rotation. Alignment of the interferometer, the CGHs, the tables and the test surface is also discussed with a reasonable layout of the whole test system. The interferometer and the near-null optics are translated by a three-axis stage while the test mirror is rotated and tilted by two rotary tables. Experimental results are finally given to show the near-null subaperture test capability of the system for a convex even asphere.

Maximum margin semi-supervised learning with irrelevant data.

PubMed

Yang, Haiqin; Huang, Kaizhu; King, Irwin; Lyu, Michael R

2015-10-01

Semi-supervised learning (SSL) is a typical learning paradigms training a model from both labeled and unlabeled data. The traditional SSL models usually assume unlabeled data are relevant to the labeled data, i.e., following the same distributions of the targeted labeled data. In this paper, we address a different, yet formidable scenario in semi-supervised classification, where the unlabeled data may contain irrelevant data to the labeled data. To tackle this problem, we develop a maximum margin model, named tri-class support vector machine (3C-SVM), to utilize the available training data, while seeking a hyperplane for separating the targeted data well. Our 3C-SVM exhibits several characteristics and advantages. First, it does not need any prior knowledge and explicit assumption on the data relatedness. On the contrary, it can relieve the effect of irrelevant unlabeled data based on the logistic principle and maximum entropy principle. That is, 3C-SVM approaches an ideal classifier. This classifier relies heavily on labeled data and is confident on the relevant data lying far away from the decision hyperplane, while maximally ignoring the irrelevant data, which are hardly distinguished. Second, theoretical analysis is provided to prove that in what condition, the irrelevant data can help to seek the hyperplane. Third, 3C-SVM is a generalized model that unifies several popular maximum margin models, including standard SVMs, Semi-supervised SVMs (S(3)VMs), and SVMs learned from the universum (U-SVMs) as its special cases. More importantly, we deploy a concave-convex produce to solve the proposed 3C-SVM, transforming the original mixed integer programming, to a semi-definite programming relaxation, and finally to a sequence of quadratic programming subproblems, which yields the same worst case time complexity as that of S(3)VMs. Finally, we demonstrate the effectiveness and efficiency of our proposed 3C-SVM through systematical experimental comparisons. Copyright © 2015 Elsevier Ltd. All rights reserved.

CometBoards Users Manual Release 1.0

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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/.

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

NASA Technical Reports Server (NTRS)

Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

2009-01-01

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

Sequential Quadratic Programming Algorithms for Optimization

DTIC Science & Technology

1989-08-01

quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the

Quadratic polynomial interpolation on triangular domain

NASA Astrophysics Data System (ADS)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

Group Variable Selection Via Convex Log-Exp-Sum Penalty with Application to a Breast Cancer Survivor Study

PubMed Central

Geng, Zhigeng; Wang, Sijian; Yu, Menggang; Monahan, Patrick O.; Champion, Victoria; Wahba, Grace

2017-01-01

Summary In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. Among existing successful group variable selection methods, some methods fail to conduct the within group selection. Some methods are able to conduct both group and within group selection, but the corresponding objective functions are non-convex. Such a non-convexity may require extra numerical effort. In this article, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting where the number of covariates can be much larger than the sample size. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and may help design intervention programs to improve the qualify of life for breast cancer survivors. PMID:25257196

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

PubMed

Khoo, Y; Singer, A; Cowburn, D

2017-07-01

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

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

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.

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).

Developing an Understanding of Quadratics through the Use of Concrete Manipulatives: A Case Study Analysis of the Metacognitive Development of a High School Student with Learning Disabilities

ERIC Educational Resources Information Center

Strickland, Tricia K.

2014-01-01

This case study analyzed the impact of a concrete manipulative program on the understanding of quadratic expressions for a high school student with a learning disability. The manipulatives were utilized as part of the Concrete-Representational-Abstract Integration (CRA-I) intervention in which participants engaged in tasks requiring them to…

Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

NASA Astrophysics Data System (ADS)

Uilhoorn, F. E.

2016-10-01

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

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

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

Bent, Rusell; Nagarajan, Harsha; Sundar, Kaarthik

2017-09-25

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

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.

SINDA'85/FLUINT - SYSTEMS IMPROVED NUMERICAL DIFFERENCING ANALYZER AND FLUID INTEGRATOR (CONVEX VERSION)

NASA Technical Reports Server (NTRS)

Cullimore, B.

1994-01-01

SINDA, the Systems Improved Numerical Differencing Analyzer, is a software system for solving lumped parameter representations of physical problems governed by diffusion-type equations. SINDA was originally designed for analyzing thermal systems represented in electrical analog, lumped parameter form, although its use may be extended to include other classes of physical systems which can be modeled in this form. As a thermal analyzer, SINDA can handle such interrelated phenomena as sublimation, diffuse radiation within enclosures, transport delay effects, and sensitivity analysis. FLUINT, the FLUid INTegrator, is an advanced one-dimensional fluid analysis program that solves arbitrary fluid flow networks. The working fluids can be single phase vapor, single phase liquid, or two phase. The SINDA'85/FLUINT system permits the mutual influences of thermal and fluid problems to be analyzed. The SINDA system consists of a programming language, a preprocessor, and a subroutine library. The SINDA language is designed for working with lumped parameter representations and finite difference solution techniques. The preprocessor accepts programs written in the SINDA language and converts them into standard FORTRAN. The SINDA library consists of a large number of FORTRAN subroutines that perform a variety of commonly needed actions. The use of these subroutines can greatly reduce the programming effort required to solve many problems. A complete run of a SINDA'85/FLUINT model is a four step process. First, the user's desired model is run through the preprocessor which writes out data files for the processor to read and translates the user's program code. Second, the translated code is compiled. The third step requires linking the user's code with the processor library. Finally, the processor is executed. SINDA'85/FLUINT program features include 20,000 nodes, 100,000 conductors, 100 thermal submodels, and 10 fluid submodels. SINDA'85/FLUINT can also model two phase flow, capillary devices, user defined fluids, gravity and acceleration body forces on a fluid, and variable volumes. SINDA'85/FLUINT offers the following numerical solution techniques. The Finite difference formulation of the explicit method is the Forward-difference explicit approximation. The formulation of the implicit method is the Crank-Nicolson approximation. The program allows simulation of non-uniform heating and facilitates modeling thin-walled heat exchangers. The ability to model non-equilibrium behavior within two-phase volumes is included. Recent improvements to the program were made in modeling real evaporator-pumps and other capillary-assist evaporators. SINDA'85/FLUINT is available by license for a period of ten (10) years to approved licensees. The licensed program product includes the source code and one copy of the supporting documentation. Additional copies of the documentation may be purchased separately at any time. SINDA'85/FLUINT is written in FORTRAN 77. Version 2.3 has been implemented on Cray series computers running UNICOS, CONVEX computers running CONVEX OS, and DEC RISC computers running ULTRIX. Binaries are included with the Cray version only. The Cray version of SINDA'85/FLUINT also contains SINGE, an additional graphics program developed at Johnson Space Flight Center. Both source and executable code are provided for SINGE. Users wishing to create their own SINGE executable will also need the NASA Device Independent Graphics Library (NASADIG, previously known as SMDDIG; UNIX version, MSC-22001). The Cray and CONVEX versions of SINDA'85/FLUINT are available on 9-track 1600 BPI UNIX tar format magnetic tapes. The CONVEX version is also available on a .25 inch streaming magnetic tape cartridge in UNIX tar format. The DEC RISC ULTRIX version is available on a TK50 magnetic tape cartridge in UNIX tar format. SINDA was developed in 1971, and first had fluid capability added in 1975. SINDA'85/FLUINT version 2.3 was released in 1990.

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

PubMed Central

Wang, Di; Kleinberg, Robert D.

2009-01-01

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

PubMed

Wang, Di; Kleinberg, Robert D

2009-11-28

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

NASA Astrophysics Data System (ADS)

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

Constrained multiple indicator kriging using sequential quadratic programming

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Erhan Tercan, A.

2012-11-01

Multiple indicator kriging (MIK) is a nonparametric method used to estimate conditional cumulative distribution functions (CCDF). Indicator estimates produced by MIK may not satisfy the order relations of a valid CCDF which is ordered and bounded between 0 and 1. In this paper a new method has been presented that guarantees the order relations of the cumulative distribution functions estimated by multiple indicator kriging. The method is based on minimizing the sum of kriging variances for each cutoff under unbiasedness and order relations constraints and solving constrained indicator kriging system by sequential quadratic programming. A computer code is written in the Matlab environment to implement the developed algorithm and the method is applied to the thickness data.

Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical parameters based on the time-domain radiative transfer equation.

PubMed

Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming

2016-10-17

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

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

Murray, W.; Prieto, F.J.

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is notmore » assumed that the iterates lie on a compact set.« less

DE and NLP Based QPLS Algorithm

NASA Astrophysics Data System (ADS)

Yu, Xiaodong; Huang, Dexian; Wang, Xiong; Liu, Bo

As a novel evolutionary computing technique, Differential Evolution (DE) has been considered to be an effective optimization method for complex optimization problems, and achieved many successful applications in engineering. In this paper, a new algorithm of Quadratic Partial Least Squares (QPLS) based on Nonlinear Programming (NLP) is presented. And DE is used to solve the NLP so as to calculate the optimal input weights and the parameters of inner relationship. The simulation results based on the soft measurement of diesel oil solidifying point on a real crude distillation unit demonstrate that the superiority of the proposed algorithm to linear PLS and QPLS which is based on Sequential Quadratic Programming (SQP) in terms of fitting accuracy and computational costs.

Static Analysis Numerical Algorithms

DTIC Science & Technology

2016-04-01

represented by a collection of intervals (one for each variable) or a convex polyhedron (each dimension of the affine space representing a program variable...Another common abstract domain uses a set of linear constraints (i.e. an enclosing polyhedron ) to over-approximate the joint values of several

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

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

Ghomi, Pooyan Shirvani; Zinchenko, Yuriy

2014-08-15

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

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.

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

PubMed

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

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.

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.

A Survey of Mathematical Programming in the Soviet Union (Bibliography),

DTIC Science & Technology

1982-01-01

ASTAFYEV, N. N., "METHOD OF LINEARIZATION IN CONVEX PROGRAMMING", TR4- Y ZIMN SHKOLY PO MAT PROGRAMMIR I XMEZHN VOPR DROGOBYCH, 72, VOL. 3, 54-73 2...AKADEMIYA KOMMUNLN’NOGO KHOZYAYSTVA (MOSCOW), 72, NO. 93, 70-77 19. GIMELFARB , G, V. MARCHENKO, V. RYBAK, "AUTOMATIC IDENTIFICATION OF IDENTICAL POINTS...DYNAMIC PROGRAMMING (CONTINUED) 25. KOLOSOV, G. Y , "ON ANALYTICAL SOLUTION OF DESIGN PROBLEMS FOR DISTRIBUTED OPTIMAL CONTROL SYSTEMS SUBJECTED TO RANDOM

Totally Asymmetric Limit for Models of Heat Conduction

NASA Astrophysics Data System (ADS)

De Carlo, Leonardo; Gabrielli, Davide

2017-08-01

We consider one dimensional weakly asymmetric boundary driven models of heat conduction. In the cases of a constant diffusion coefficient and of a quadratic mobility we compute the quasi-potential that is a non local functional obtained by the solution of a variational problem. This is done using the dynamic variational approach of the macroscopic fluctuation theory (Bertini et al. in Rev Mod Phys 87:593, 2015). The case of a concave mobility corresponds essentially to the exclusion model that has been discussed in Bertini et al. (J Stat Mech L11001, 2010; Pure Appl Math 64(5):649-696, 2011; Commun Math Phys 289(1):311-334, 2009) and Enaud and Derrida (J Stat Phys 114:537-562, 2004). We consider here the convex case that includes for example the Kipnis-Marchioro-Presutti (KMP) model and its dual (KMPd) (Kipnis et al. in J Stat Phys 27:6574, 1982). This extends to the weakly asymmetric regime the computations in Bertini et al. (J Stat Phys 121(5/6):843-885, 2005). We consider then, both microscopically and macroscopically, the limit of large externalfields. Microscopically we discuss some possible totally asymmetric limits of the KMP model. In one case the totally asymmetric dynamics has a product invariant measure. Another possible limit dynamics has instead a non trivial invariant measure for which we give a duality representation. Macroscopically we show that the quasi-potentials of KMP and KMPd, which are non local for any value of the external field, become local in the limit. Moreover the dependence on one of the external reservoirs disappears. For models having strictly positive quadratic mobilities we obtain instead in the limit a non local functional having a structure similar to the one of the boundary driven asymmetric exclusion process.

Factorization method of quadratic template

NASA Astrophysics Data System (ADS)

Kotyrba, Martin

2017-07-01

Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

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

NASA Technical Reports Server (NTRS)

Ortiz, Francisco

2004-01-01

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

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

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

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

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.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

Non-fragile observer-based output feedback control for polytopic uncertain system under distributed model predictive control approach

NASA Astrophysics Data System (ADS)

Zhu, Kaiqun; Song, Yan; Zhang, Sunjie; Zhong, Zhaozhun

2017-07-01

In this paper, a non-fragile observer-based output feedback control problem for the polytopic uncertain system under distributed model predictive control (MPC) approach is discussed. By decomposing the global system into some subsystems, the computation complexity is reduced, so it follows that the online designing time can be saved.Moreover, an observer-based output feedback control algorithm is proposed in the framework of distributed MPC to deal with the difficulties in obtaining the states measurements. In this way, the presented observer-based output-feedback MPC strategy is more flexible and applicable in practice than the traditional state-feedback one. What is more, the non-fragility of the controller has been taken into consideration in favour of increasing the robustness of the polytopic uncertain system. After that, a sufficient stability criterion is presented by using Lyapunov-like functional approach, meanwhile, the corresponding control law and the upper bound of the quadratic cost function are derived by solving an optimisation subject to convex constraints. Finally, some simulation examples are employed to show the effectiveness of the method.

Hessian Schatten-norm regularization for linear inverse problems.

PubMed

Lefkimmiatis, Stamatios; Ward, John Paul; Unser, Michael

2013-05-01

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which are computed at every pixel of the image. They can be viewed as second-order extensions of the popular total-variation (TV) semi-norm since they satisfy the same invariance properties. Meanwhile, by taking advantage of second-order derivatives, they avoid the staircase effect, a common artifact of TV-based reconstructions, and perform well for a wide range of applications. To solve the corresponding optimization problems, we propose an algorithm that is based on a primal-dual formulation. A fundamental ingredient of this algorithm is the projection of matrices onto Schatten norm balls of arbitrary radius. This operation is performed efficiently based on a direct link we provide between vector projections onto lq norm balls and matrix projections onto Schatten norm balls. Finally, we demonstrate the effectiveness of the proposed methods through experimental results on several inverse imaging problems with real and simulated data.

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.

Design and cost analysis of rapid aquifer restoration systems using flow simulation and quadratic programming.

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1986-01-01

Detailed two-dimensional flow simulation of a complex ground-water system is combined with quadratic and linear programming to evaluate design alternatives for rapid aquifer restoration. Results show how treatment and pumping costs depend dynamically on the type of treatment process, and capacity of pumping and injection wells, and the number of wells. The design for an inexpensive treatment process minimizes pumping costs, while an expensive process results in the minimization of treatment costs. Substantial reductions in pumping costs occur with increases in injection capacity or in the number of wells. Treatment costs are reduced by expansions in pumping capacity or injecion capacity. The analysis identifies maximum pumping and injection capacities.-from Authors

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

Solution Methods for Stochastic Dynamic Linear Programs.

DTIC Science & Technology

1980-12-01

16, No. 11, pp. 652-675, July 1970. [28] Glassey, C.R., "Dynamic linear programs for production scheduling", OR 19, pp. 45-56. 1971 . 129 Glassey, C.R...Huang, C.C., I. Vertinsky, W.T. Ziemba, ’Sharp bounds on the value of perfect information", OR 25, pp. 128-139, 1977. [37 Kall , P., ’Computational... 1971 . [701 Ziemba, W.T., *Computational algorithms for convex stochastic programs with simple recourse", OR 8, pp. 414-431, 1970. 131 UNCLASSI FIED

BROJA-2PID: A Robust Estimator for Bivariate Partial Information Decomposition

NASA Astrophysics Data System (ADS)

Makkeh, Abdullah; Theis, Dirk; Vicente, Raul

2018-04-01

Makkeh, Theis, and Vicente found in [8] that Cone Programming model is the most robust to compute the Bertschinger et al. partial information decompostion (BROJA PID) measure [1]. We developed a production-quality robust software that computes the BROJA PID measure based on the Cone Programming model. In this paper, we prove the important property of strong duality for the Cone Program and prove an equivalence between the Cone Program and the original Convex problem. Then describe in detail our software and how to use it.\

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.

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.

Replicator equations, maximal cliques, and graph isomorphism.

PubMed

Pelillo, M

1999-11-15

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations--a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.

Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

NASA Astrophysics Data System (ADS)

Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

2016-08-01

Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

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...

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.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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…

Airfoil

DOEpatents

Ristau, Neil; Siden, Gunnar Leif

2015-07-21

An airfoil includes a leading edge, a trailing edge downstream from the leading edge, a pressure surface between the leading and trailing edges, and a suction surface between the leading and trailing edges and opposite the pressure surface. A first convex section on the suction surface decreases in curvature downstream from the leading edge, and a throat on the suction surface is downstream from the first convex section. A second convex section is on the suction surface downstream from the throat, and a first convex segment of the second convex section increases in curvature.

FMCSA’s advanced system testing utilizing a data acquisition system on the highways (FAST DASH) safety technology evaluation project #3 : novel convex mirrors : technology brief.

DOT National Transportation Integrated Search

2016-11-01

The Federal Motor Carrier Safety Administration (FMCSA) established the FAST DASH program to perform efficient independent evaluations of promising safety technologies aimed at commercial vehicle operations. In this third FAST DASH safety technology ...

Superiorization with level control

NASA Astrophysics Data System (ADS)

Cegielski, Andrzej; Al-Musallam, Fadhel

2017-04-01

The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

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

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com; Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr; Çelik, Nuri, E-mail: ncelik@bartin.edu.tr

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

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.

Obstacle avoidance handling and mixed integer predictive control for space robots

NASA Astrophysics Data System (ADS)

Zong, Lijun; Luo, Jianjun; Wang, Mingming; Yuan, Jianping

2018-04-01

This paper presents a novel obstacle avoidance constraint and a mixed integer predictive control (MIPC) method for space robots avoiding obstacles and satisfying physical limits during performing tasks. Firstly, a novel kind of obstacle avoidance constraint of space robots, which needs the assumption that the manipulator links and the obstacles can be represented by convex bodies, is proposed by limiting the relative velocity between two closest points which are on the manipulator and the obstacle, respectively. Furthermore, the logical variables are introduced into the obstacle avoidance constraint, which have realized the constraint form is automatically changed to satisfy different obstacle avoidance requirements in different distance intervals between the space robot and the obstacle. Afterwards, the obstacle avoidance constraint and other system physical limits, such as joint angle ranges, the amplitude boundaries of joint velocities and joint torques, are described as inequality constraints of a quadratic programming (QP) problem by using the model predictive control (MPC) method. To guarantee the feasibility of the obtained multi-constraint QP problem, the constraints are treated as soft constraints and assigned levels of priority based on the propositional logic theory, which can realize that the constraints with lower priorities are always firstly violated to recover the feasibility of the QP problem. Since the logical variables have been introduced, the optimization problem including obstacle avoidance and system physical limits as prioritized inequality constraints is termed as MIPC method of space robots, and its computational complexity as well as possible strategies for reducing calculation amount are analyzed. Simulations of the space robot unfolding its manipulator and tracking the end-effector's desired trajectories with the existence of obstacles and physical limits are presented to demonstrate the effectiveness of the proposed obstacle avoidance strategy and MIPC control method of space robots.

Support Vector Hazards Machine: A Counting Process Framework for Learning Risk Scores for Censored Outcomes.

PubMed

Wang, Yuanjia; Chen, Tianle; Zeng, Donglin

2016-01-01

Learning risk scores to predict dichotomous or continuous outcomes using machine learning approaches has been studied extensively. However, how to learn risk scores for time-to-event outcomes subject to right censoring has received little attention until recently. Existing approaches rely on inverse probability weighting or rank-based regression, which may be inefficient. In this paper, we develop a new support vector hazards machine (SVHM) approach to predict censored outcomes. Our method is based on predicting the counting process associated with the time-to-event outcomes among subjects at risk via a series of support vector machines. Introducing counting processes to represent time-to-event data leads to a connection between support vector machines in supervised learning and hazards regression in standard survival analysis. To account for different at risk populations at observed event times, a time-varying offset is used in estimating risk scores. The resulting optimization is a convex quadratic programming problem that can easily incorporate non-linearity using kernel trick. We demonstrate an interesting link from the profiled empirical risk function of SVHM to the Cox partial likelihood. We then formally show that SVHM is optimal in discriminating covariate-specific hazard function from population average hazard function, and establish the consistency and learning rate of the predicted risk using the estimated risk scores. Simulation studies show improved prediction accuracy of the event times using SVHM compared to existing machine learning methods and standard conventional approaches. Finally, we analyze two real world biomedical study data where we use clinical markers and neuroimaging biomarkers to predict age-at-onset of a disease, and demonstrate superiority of SVHM in distinguishing high risk versus low risk subjects.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.

PubMed

O'Reilly, Paul G; Wen, Qing; Bankhead, Peter; Dunne, Philip D; McArt, Darragh G; McPherson, Suzanne; Hamilton, Peter W; Mills, Ken I; Zhang, Shu-Dong

2016-05-04

Gene expression connectivity mapping has proven to be a powerful and flexible tool for research. Its application has been shown in a broad range of research topics, most commonly as a means of identifying potential small molecule compounds, which may be further investigated as candidates for repurposing to treat diseases. The public release of voluminous data from the Library of Integrated Cellular Signatures (LINCS) programme further enhanced the utilities and potentials of gene expression connectivity mapping in biomedicine. We describe QUADrATiC ( http://go.qub.ac.uk/QUADrATiC ), a user-friendly tool for the exploration of gene expression connectivity on the subset of the LINCS data set corresponding to FDA-approved small molecule compounds. It enables the identification of compounds for repurposing therapeutic potentials. The software is designed to cope with the increased volume of data over existing tools, by taking advantage of multicore computing architectures to provide a scalable solution, which may be installed and operated on a range of computers, from laptops to servers. This scalability is provided by the use of the modern concurrent programming paradigm provided by the Akka framework. The QUADrATiC Graphical User Interface (GUI) has been developed using advanced Javascript frameworks, providing novel visualization capabilities for further analysis of connections. There is also a web services interface, allowing integration with other programs or scripts. QUADrATiC has been shown to provide an improvement over existing connectivity map software, in terms of scope (based on the LINCS data set), applicability (using FDA-approved compounds), usability and speed. It offers potential to biological researchers to analyze transcriptional data and generate potential therapeutics for focussed study in the lab. QUADrATiC represents a step change in the process of investigating gene expression connectivity and provides more biologically-relevant results than previous alternative solutions.

CAD-based Automatic Modeling Method for Geant4 geometry model Through MCAM

NASA Astrophysics Data System (ADS)

Wang, Dong; Nie, Fanzhi; Wang, Guozhong; Long, Pengcheng; LV, Zhongliang; LV, Zhongliang

2014-06-01

Geant4 is a widely used Monte Carlo transport simulation package. Before calculating using Geant4, the calculation model need be established which could be described by using Geometry Description Markup Language (GDML) or C++ language. However, it is time-consuming and error-prone to manually describe the models by GDML. Automatic modeling methods have been developed recently, but there are some problem existed in most of present modeling programs, specially some of them were not accurate or adapted to specifically CAD format. To convert the GDML format models to CAD format accurately, a Geant4 Computer Aided Design (CAD) based modeling method was developed for automatically converting complex CAD geometry model into GDML geometry model. The essence of this method was dealing with CAD model represented with boundary representation (B-REP) and GDML model represented with constructive solid geometry (CSG). At first, CAD model was decomposed to several simple solids which had only one close shell. And then the simple solid was decomposed to convex shell set. Then corresponding GDML convex basic solids were generated by the boundary surfaces getting from the topological characteristic of a convex shell. After the generation of these solids, GDML model was accomplished with series boolean operations. This method was adopted in CAD/Image-based Automatic Modeling Program for Neutronics & Radiation Transport (MCAM), and tested with several models including the examples in Geant4 install package. The results showed that this method could convert standard CAD model accurately, and can be used for Geant4 automatic modeling.

AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L. C.

1984-01-01

AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

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.

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.

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

DTIC Science & Technology

1982-12-21

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

Algorithms for Maneuvering Spacecraft Around Small Bodies

NASA Technical Reports Server (NTRS)

Acikmese, A. Bechet; Bayard, David

2006-01-01

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

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.

First Evaluation of the New Thin Convex Probe Endobronchial Ultrasound Scope: A Human Ex Vivo Lung Study.

PubMed

Patel, Priya; Wada, Hironobu; Hu, Hsin-Pei; Hirohashi, Kentaro; Kato, Tatsuya; Ujiie, Hideki; Ahn, Jin Young; Lee, Daiyoon; Geddie, William; Yasufuku, Kazuhiro

2017-04-01

Endobronchial ultrasonography (EBUS)-guided transbronchial needle aspiration allows for sampling of mediastinal lymph nodes. The external diameter, rigidity, and angulation of the convex probe EBUS renders limited accessibility. This study compares the accessibility and transbronchial needle aspiration capability of the prototype thin convex probe EBUS against the convex probe EBUS in human ex vivo lungs rejected for transplant. The prototype thin convex probe EBUS (BF-Y0055; Olympus, Tokyo, Japan) with a thinner tip (5.9 mm), greater upward angle (170 degrees), and decreased forward oblique direction of view (20 degrees) was compared with the current convex probe EBUS (6.9-mm tip, 120 degrees, and 35 degrees, respectively). Accessibility and transbronchial needle aspiration capability was assessed in ex vivo human lungs declined for lung transplant. The distance of maximum reach and sustainable endoscopic limit were measured. Transbronchial needle aspiration capability was assessed using the prototype 25G aspiration needle in segmental lymph nodes. In all evaluated lungs (n = 5), the thin convex probe EBUS demonstrated greater reach and a higher success rate, averaging 22.1 mm greater maximum reach and 10.3 mm further endoscopic visibility range than convex probe EBUS, and could assess selectively almost all segmental bronchi (98% right, 91% left), demonstrating nearly twice the accessibility as the convex probe EBUS (48% right, 47% left). The prototype successfully enabled cytologic assessment of subsegmental lymph nodes with adequate quality using the dedicated 25G aspiration needle. Thin convex probe EBUS has greater accessibility to peripheral airways in human lungs and is capable of sampling segmental lymph nodes using the aspiration needle. That will allow for more precise assessment of N1 nodes and, possibly, intrapulmonary lesions normally inaccessible to the conventional convex probe EBUS. Copyright © 2017 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

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

NASA Astrophysics Data System (ADS)

Parmar, Jupinder; Rahman, Saarim; Thiara, Jaskaran

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

Support Vector Machine algorithm for regression and classification

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

Yu, Chenggang; Zavaljevski, Nela

2001-08-01

The software is an implementation of the Support Vector Machine (SVM) algorithm that was invented and developed by Vladimir Vapnik and his co-workers at AT&T Bell Laboratories. The specific implementation reported here is an Active Set method for solving a quadratic optimization problem that forms the major part of any SVM program. The implementation is tuned to specific constraints generated in the SVM learning. Thus, it is more efficient than general-purpose quadratic optimization programs. A decomposition method has been implemented in the software that enables processing large data sets. The size of the learning data is virtually unlimited by themore » capacity of the computer physical memory. The software is flexible and extensible. Two upper bounds are implemented to regulate the SVM learning for classification, which allow users to adjust the false positive and false negative rates. The software can be used either as a standalone, general-purpose SVM regression or classification program, or be embedded into a larger software system.« less

Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

PubMed Central

Serang, Oliver

2012-01-01

Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics. PMID:22952741

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

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

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Quantum optimization for training support vector machines.

PubMed

Anguita, Davide; Ridella, Sandro; Rivieccio, Fabio; Zunino, Rodolfo

2003-01-01

Refined concepts, such as Rademacher estimates of model complexity and nonlinear criteria for weighting empirical classification errors, represent recent and promising approaches to characterize the generalization ability of Support Vector Machines (SVMs). The advantages of those techniques lie in both improving the SVM representation ability and yielding tighter generalization bounds. On the other hand, they often make Quadratic-Programming algorithms no longer applicable, and SVM training cannot benefit from efficient, specialized optimization techniques. The paper considers the application of Quantum Computing to solve the problem of effective SVM training, especially in the case of digital implementations. The presented research compares the behavioral aspects of conventional and enhanced SVMs; experiments in both a synthetic and real-world problems support the theoretical analysis. At the same time, the related differences between Quadratic-Programming and Quantum-based optimization techniques are considered.

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

NASA Astrophysics Data System (ADS)

Virgili-Llop, Josep; Zagaris, Costantinos; Park, Hyeongjun; Zappulla, Richard; Romano, Marcello

2018-03-01

An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a ground-based air-bearing test bed, using spacecraft simulators that float over a granite table.

Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization

NASA Astrophysics Data System (ADS)

Yamagishi, Masao; Yamada, Isao

2017-04-01

Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.

A reduced successive quadratic programming strategy for errors-in-variables estimation.

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

Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

Radius of convexity of a certain class of close-to-convex functions

NASA Astrophysics Data System (ADS)

Yahya, Abdullah; Soh, Shaharuddin Cik

2017-11-01

In the present paper, we consider and investigate a certain class of close-to-convex functions that defined in the unit disk, U = {z : |z| < 1}, which denotes as Re { ei αz/f '(z ) f (z )-f (-z ) } >δ where |α| < π, cos (α) > δ and 0 δ <1. Furthermore, we obtain preliminary result for bound f'(z) and determine result for radius of convexity.

Convex Graph Invariants

DTIC Science & Technology

2010-12-02

Motzkin, T. and Straus, E. (1965). Maxima for graphs and a new proof of a theorem of Turan . Canad. J. Math. 17 533–540. [33] Rendl, F. and Sotirov, R...Convex Graph Invariants Venkat Chandrasekaran, Pablo A . Parrilo, and Alan S. Willsky ∗ Laboratory for Information and Decision Systems Department of...this paper we study convex graph invariants, which are graph invariants that are convex functions of the adjacency matrix of a graph. Some examples

Allometric relationships between traveltime channel networks, convex hulls, and convexity measures

NASA Astrophysics Data System (ADS)

Tay, Lea Tien; Sagar, B. S. Daya; Chuah, Hean Teik

2006-06-01

The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and areas of corresponding convex hulls C(Sn), the ratios of which provide convexity measures CM(Sn) of traveltime networks. A statistically significant scaling relationship is found for a model network in the form L(Sn) ˜ A[C(Sn)]0.57. From the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures, new power law relations are derived. Such relations for a model network are CM(Sn) ˜ ? and CM(Sn) ˜ ?. In addition to the model study, these relations for networks derived from seven subbasins of Cameron Highlands region of Peninsular Malaysia are provided. Further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks.

An algorithm for the solution of dynamic linear programs

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1989-01-01

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

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.

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

The Comparison Study of Quadratic Infinite Beam Program on Optimization Instensity Modulated Radiation Therapy Treatment Planning (IMRTP) between Threshold and Exponential Scatter Method with CERR® In The Case of Lung Cancer

NASA Astrophysics Data System (ADS)

Hardiyanti, Y.; Haekal, M.; Waris, A.; Haryanto, F.

2016-08-01

This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin.

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.

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.

An Improved Search Approach for Solving Non-Convex Mixed-Integer Non Linear Programming Problems

NASA Astrophysics Data System (ADS)

Sitopu, Joni Wilson; Mawengkang, Herman; Syafitri Lubis, Riri

2018-01-01

The nonlinear mathematical programming problem addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method, has been developed. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Successful implementation of these algorithms was achieved on various test problems.

Convex Relaxation For Hard Problem In Data Mining And Sensor Localization

DTIC Science & Technology

2017-04-13

Drusvyatskiy, S.A. Vavasis, and H. Wolkowicz. Extreme point in- equalities and geometry of the rank sparsity ball. Math . Program., 152(1-2, Ser. A...521–544, 2015. [3] M-H. Lin and H. Wolkowicz. Hiroshima’s theorem and matrix norm inequalities. Acta Sci. Math . (Szeged), 81(1-2):45–53, 2015. [4] D...9867-4. [8] D. Drusvyatskiy, G. Li, and H. Wolkowicz. Alternating projections for ill-posed semidenite feasibility problems. Math . Program., 2016

One cutting plane algorithm using auxiliary functions

NASA Astrophysics Data System (ADS)

Zabotin, I. Ya; Kazaeva, K. E.

2016-11-01

We propose an algorithm for solving a convex programming problem from the class of cutting methods. The algorithm is characterized by the construction of approximations using some auxiliary functions, instead of the objective function. Each auxiliary function bases on the exterior penalty function. In proposed algorithm the admissible set and the epigraph of each auxiliary function are embedded into polyhedral sets. In connection with the above, the iteration points are found by solving linear programming problems. We discuss the implementation of the algorithm and prove its convergence.

On Viviani's Theorem and Its Extensions

ERIC Educational Resources Information Center

Abboud, Elias

2010-01-01

Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…

Feature Grouping and Selection Over an Undirected Graph.

PubMed

Yang, Sen; Yuan, Lei; Lai, Ying-Cheng; Shen, Xiaotong; Wonka, Peter; Ye, Jieping

2012-01-01

High-dimensional regression/classification continues to be an important and challenging problem, especially when features are highly correlated. Feature selection, combined with additional structure information on the features has been considered to be promising in promoting regression/classification performance. Graph-guided fused lasso (GFlasso) has recently been proposed to facilitate feature selection and graph structure exploitation, when features exhibit certain graph structures. However, the formulation in GFlasso relies on pairwise sample correlations to perform feature grouping, which could introduce additional estimation bias. In this paper, we propose three new feature grouping and selection methods to resolve this issue. The first method employs a convex function to penalize the pairwise l ∞ norm of connected regression/classification coefficients, achieving simultaneous feature grouping and selection. The second method improves the first one by utilizing a non-convex function to reduce the estimation bias. The third one is the extension of the second method using a truncated l 1 regularization to further reduce the estimation bias. The proposed methods combine feature grouping and feature selection to enhance estimation accuracy. We employ the alternating direction method of multipliers (ADMM) and difference of convex functions (DC) programming to solve the proposed formulations. Our experimental results on synthetic data and two real datasets demonstrate the effectiveness of the proposed methods.

Maximum Margin Clustering of Hyperspectral Data

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

Distributed reconfigurable control strategies for switching topology networked multi-agent systems.

PubMed

Gallehdari, Z; Meskin, N; Khorasani, K

2017-11-01

In this paper, distributed control reconfiguration strategies for directed switching topology networked multi-agent systems are developed and investigated. The proposed control strategies are invoked when the agents are subject to actuator faults and while the available fault detection and isolation (FDI) modules provide inaccurate and unreliable information on the estimation of faults severities. Our proposed strategies will ensure that the agents reach a consensus while an upper bound on the team performance index is ensured and satisfied. Three types of actuator faults are considered, namely: the loss of effectiveness fault, the outage fault, and the stuck fault. By utilizing quadratic and convex hull (composite) Lyapunov functions, two cooperative and distributed recovery strategies are designed and provided to select the gains of the proposed control laws such that the team objectives are guaranteed. Our proposed reconfigurable control laws are applied to a team of autonomous underwater vehicles (AUVs) under directed switching topologies and subject to simultaneous actuator faults. Simulation results demonstrate the effectiveness of our proposed distributed reconfiguration control laws in compensating for the effects of sudden actuator faults and subject to fault diagnosis module uncertainties and unreliabilities. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Model Predictive Control considering Reachable Range of Wheels for Leg / Wheel Mobile Robots

NASA Astrophysics Data System (ADS)

Suzuki, Naito; Nonaka, Kenichiro; Sekiguchi, Kazuma

2016-09-01

Obstacle avoidance is one of the important tasks for mobile robots. In this paper, we study obstacle avoidance control for mobile robots equipped with four legs comprised of three DoF SCARA leg/wheel mechanism, which enables the robot to change its shape adapting to environments. Our previous method achieves obstacle avoidance by model predictive control (MPC) considering obstacle size and lateral wheel positions. However, this method does not ensure existence of joint angles which achieves reference wheel positions calculated by MPC. In this study, we propose a model predictive control considering reachable mobile ranges of wheels positions by combining multiple linear constraints, where each reachable mobile range is approximated as a convex trapezoid. Thus, we achieve to formulate a MPC as a quadratic problem with linear constraints for nonlinear problem of longitudinal and lateral wheel position control. By optimization of MPC, the reference wheel positions are calculated, while each joint angle is determined by inverse kinematics. Considering reachable mobile ranges explicitly, the optimal joint angles are calculated, which enables wheels to reach the reference wheel positions. We verify its advantages by comparing the proposed method with the previous method through numerical simulations.

The transition of a real-time single-rotor helicopter simulation program to a supercomputer

NASA Technical Reports Server (NTRS)

Martinez, Debbie

1995-01-01

This report presents the conversion effort and results of a real-time flight simulation application transition to a CONVEX supercomputer. Enclosed is a detailed description of the conversion process and a brief description of the Langley Research Center's (LaRC) flight simulation application program structure. Currently, this simulation program may be configured to represent Sikorsky S-61 helicopter (a five-blade, single-rotor, commercial passenger-type helicopter) or an Army Cobra helicopter (either the AH-1 G or AH-1 S model). This report refers to the Sikorsky S-61 simulation program since it is the most frequently used configuration.

About the mechanism of ERP-system pilot test

NASA Astrophysics Data System (ADS)

Mitkov, V. V.; Zimin, V. V.

2018-05-01

In the paper the mathematical problem of defining the scope of pilot test is stated, which is a task of quadratic programming. The procedure of the problem solving includes the method of network programming based on the structurally similar network representation of the criterion and constraints and which reduces the original problem to a sequence of simpler evaluation tasks. The evaluation tasks are solved by the method of dichotomous programming.

Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis

DTIC Science & Technology

2016-10-11

Analysis of Interior Point Algorithms for Non-Lipschitz and Nonconvex Minimization,” (W. Bian, X. Chen, and Ye), Math Programming, 149 (2015) 301-327...Chen, Ge, Wang, Ye), Math Programming, 143 (1-2) (2014) 371-383. This paper resolved an important open question in cardinality constrained...Statistical Performance, and Algorithmic Theory for Local Solutions,” (H. Liu, T. Yao, R. Li, Y. Ye) manuscript, 2nd revision in Math Programming

CVXPY: A Python-Embedded Modeling Language for Convex Optimization.

PubMed

Diamond, Steven; Boyd, Stephen

2016-04-01

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

Usefulness of the convexity apparent hyperperfusion sign in 123I-iodoamphetamine brain perfusion SPECT for the diagnosis of idiopathic normal pressure hydrocephalus.

PubMed

Ohmichi, Takuma; Kondo, Masaki; Itsukage, Masahiro; Koizumi, Hidetaka; Matsushima, Shigenori; Kuriyama, Nagato; Ishii, Kazunari; Mori, Etsuro; Yamada, Kei; Mizuno, Toshiki; Tokuda, Takahiko

2018-03-16

OBJECTIVE The gold standard for the diagnosis of idiopathic normal pressure hydrocephalus (iNPH) is the CSF removal test. For elderly patients, however, a less invasive diagnostic method is required. On MRI, high-convexity tightness was reported to be an important finding for the diagnosis of iNPH. On SPECT, patients with iNPH often show hyperperfusion of the high-convexity area. The authors tested 2 hypotheses regarding the SPECT finding: 1) it is relative hyperperfusion reflecting the increased gray matter density of the convexity, and 2) it is useful for the diagnosis of iNPH. The authors termed the SPECT finding the convexity apparent hyperperfusion (CAPPAH) sign. METHODS Two clinical studies were conducted. In study 1, SPECT was performed for 20 patients suspected of having iNPH, and regional cerebral blood flow (rCBF) of the high-convexity area was examined using quantitative analysis. Clinical differences between patients with the CAPPAH sign (CAP) and those without it (NCAP) were also compared. In study 2, the CAPPAH sign was retrospectively assessed in 30 patients with iNPH and 19 healthy controls using SPECT images and 3D stereotactic surface projection. RESULTS In study 1, rCBF of the high-convexity area of the CAP group was calculated as 35.2-43.7 ml/min/100 g, which is not higher than normal values of rCBF determined by SPECT. The NCAP group showed lower cognitive function and weaker responses to the removal of CSF than the CAP group. In study 2, the CAPPAH sign was positive only in patients with iNPH (24/30) and not in controls (sensitivity 80%, specificity 100%). The coincidence rate between tight high convexity on MRI and the CAPPAH sign was very high (28/30). CONCLUSIONS Patients with iNPH showed hyperperfusion of the high-convexity area on SPECT; however, the presence of the CAPPAH sign did not indicate real hyperperfusion of rCBF in the high-convexity area. The authors speculated that patients with iNPH without the CAPPAH sign, despite showing tight high convexity on MRI, might have comorbidities such as Alzheimer's disease.

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

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

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

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

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

NASA Technical Reports Server (NTRS)

Badavi, F. F.; Everhart, Joel L.

1987-01-01

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

A duality theorem-based algorithm for inexact quadratic programming problems: Application to waste management under uncertainty

NASA Astrophysics Data System (ADS)

Kong, X. M.; Huang, G. H.; Fan, Y. R.; Li, Y. P.

2016-04-01

In this study, a duality theorem-based algorithm (DTA) for inexact quadratic programming (IQP) is developed for municipal solid waste (MSW) management under uncertainty. It improves upon the existing numerical solution method for IQP problems. The comparison between DTA and derivative algorithm (DAM) shows that the DTA method provides better solutions than DAM with lower computational complexity. It is not necessary to identify the uncertain relationship between the objective function and decision variables, which is required for the solution process of DAM. The developed method is applied to a case study of MSW management and planning. The results indicate that reasonable solutions have been generated for supporting long-term MSW management and planning. They could provide more information as well as enable managers to make better decisions to identify desired MSW management policies in association with minimized cost under uncertainty.

CVXPY: A Python-Embedded Modeling Language for Convex Optimization

PubMed Central

Diamond, Steven; Boyd, Stephen

2016-01-01

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

A 'range test' for determining scatterers with unknown physical properties

NASA Astrophysics Data System (ADS)

Potthast, Roland; Sylvester, John; Kusiak, Steven

2003-06-01

We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subset of the scatterer and provides information about its location and estimates for its shape. For convex polygonal scatterers the scattering support coincides with the scatterer and we obtain full shape reconstructions. The method will be formulated for the reconstruction of the scatterers from the far field pattern for one or a few incident waves. The method is non-iterative in nature and belongs to the type of recently derived generalized sampling schemes such as the 'no response test' of Luke-Potthast. The range test operates by testing whether it is possible to analytically continue a far field to the exterior of any test domain Omegatest. By intersecting the convex hulls of various test domains we can produce a minimal convex set, the convex scattering support of which must be contained in the convex hull of the support of any scatterer which produces that far field. The convex scattering support is calculated by testing the range of special integral operators for a sampling set of test domains. The numerical results can be used as an approximation for the support of the unknown scatterer. We prove convergence and regularity of the scheme and show numerical examples for sound-soft, sound-hard and medium scatterers. We can apply the range test to non-convex scatterers as well. We can conclude that an Omegatest which passes the range test has a non-empty intersection with the infinity-support (the complement of the unbounded component of the complement of the support) of the true scatterer, but cannot find a minimal set which must be contained therein.

Duality of caustics in Minkowski billiards

NASA Astrophysics Data System (ADS)

Artstein-Avidan, S.; Florentin, D. I.; Ostrover, Y.; Rosen, D.

2018-04-01

In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth, centrally symmetric, strictly convex body K, for every convex caustic which K possesses, the ‘dual’ billiard dynamics in which the table is the Euclidean unit ball and the geometry that governs the motion is induced by the body K, possesses a dual convex caustic. Such a pair of caustics are dual in a strong sense, and in particular they have the same perimeter, Lazutkin parameter (both measured with respect to the corresponding geometries), and rotation number. We show moreover that for general Minkowski billiards this phenomenon fails, and one can construct a smooth caustic in a Minkowski billiard table which possesses no dual convex caustic.

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.

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.

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.

Assessing the influence of lower facial profile convexity on perceived attractiveness in the orthognathic patient, clinician, and layperson.

PubMed

Naini, Farhad B; Donaldson, Ana Nora A; McDonald, Fraser; Cobourne, Martyn T

2012-09-01

The aim was a quantitative evaluation of how the severity of lower facial profile convexity influences perceived attractiveness. The lower facial profile of an idealized image was altered incrementally between 14° to -16°. Images were rated on a Likert scale by orthognathic patients, laypeople, and clinicians. Attractiveness ratings were greater for straight profiles in relation to convex/concave, with no significant difference between convex and concave profiles. Ratings decreased by 0.23 of a level for every degree increase in the convexity angle. Class II/III patients gave significantly reduced ratings of attractiveness and had greater desire for surgery than class I. A straight profile is perceived as most attractive and greater degrees of convexity or concavity deemed progressively less attractive, but a range of 10° to -12° may be deemed acceptable; beyond these values surgical correction is desired. Patients are most critical, and clinicians are more critical than laypeople. Copyright © 2012 Elsevier Inc. All rights reserved.

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

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

Papp, D; Unkelbach, J

2014-06-01

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

Trading strategies for distribution company with stochastic distributed energy resources

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

Zhang, Chunyu; Wang, Qi; Wang, Jianhui

2016-09-01

This paper proposes a methodology to address the trading strategies of a proactive distribution company (PDISCO) engaged in the transmission-level (TL) markets. A one-leader multi-follower bilevel model is presented to formulate the gaming framework between the PDISCO and markets. The lower-level (LL) problems include the TL day-ahead market and scenario-based real-time markets, respectively with the objectives of maximizing social welfare and minimizing operation cost. The upper-level (UL) problem is to maximize the PDISCO’s profit across these markets. The PDISCO’s strategic offers/bids interactively influence the outcomes of each market. Since the LL problems are linear and convex, while the UL problemmore » is non-linear and non-convex, an equivalent primal–dual approach is used to reformulate this bilevel model to a solvable mathematical program with equilibrium constraints (MPEC). The effectiveness of the proposed model is verified by case studies.« less

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

NASA Astrophysics Data System (ADS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

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.

Quadrat Data for Fermilab Prairie Plant Survey

Science.gov Websites

Quadrat Data 2012 Quadrat Data 2013 Quadrat Data None taken by volunteers in 2014 due to weather problems . 2015 Quadrat Data 2016 Quadrat Data None taken by volunteers in 2017 due to weather and other problems

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.

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.

A STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD FOR CONVEX PROGRAMMING.

PubMed

Bingsheng, He; Liu, Han; Wang, Zhaoran; Yuan, Xiaoming

2014-07-01

In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its convergence, while it is always faster whenever it is convergent. We first illustrate that the reason for this difference is that the iterative sequence generated by DRSM is strictly contractive, while that generated by PRSM is only contractive with respect to the solution set of the model. With only the convexity assumption on the objective function of the model under consideration, the convergence of PRSM is not guaranteed. But for this case, we show that the first t iterations of PRSM still enable us to find an approximate solution with an accuracy of O (1/ t ). A worst-case O (1/ t ) convergence rate of PRSM in the ergodic sense is thus established under mild assumptions. After that, we suggest attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and thus propose a strictly contractive PRSM. A worst-case O (1/ t ) convergence rate of this strictly contractive PRSM in a nonergodic sense is established. We show the numerical efficiency of the strictly contractive PRSM by some applications in statistical learning and image processing.

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

PubMed

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

2017-09-18

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

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

PubMed Central

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

2017-01-01

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

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

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

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

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

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

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.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

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

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

A Generalized Distance’ Estimation Procedure for Intra-Urban Interaction

DTIC Science & Technology

Bettinger . It is found that available estimation techniques necessarily result in non-integer solutions. A mathematical device is therefore...The estimation of urban and regional travel patterns has been a necessary part of current efforts to establish land use guidelines for the Texas...paper details computational experience with travel estimation within Corpus Christi, Texas, using a new convex programming approach of Charnes, Raike and

Solution of quadratic matrix equations for free vibration analysis of structures.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

VASP- VARIABLE DIMENSION AUTOMATIC SYNTHESIS PROGRAM

NASA Technical Reports Server (NTRS)

White, J. S.

1994-01-01

VASP is a variable dimension Fortran version of the Automatic Synthesis Program, ASP. The program is used to implement Kalman filtering and control theory. Basically, it consists of 31 subprograms for solving most modern control problems in linear, time-variant (or time-invariant) control systems. These subprograms include operations of matrix algebra, computation of the exponential of a matrix and its convolution integral, and the solution of the matrix Riccati equation. The user calls these subprograms by means of a FORTRAN main program, and so can easily obtain solutions to most general problems of extremization of a quadratic functional of the state of the linear dynamical system. Particularly, these problems include the synthesis of the Kalman filter gains and the optimal feedback gains for minimization of a quadratic performance index. VASP, as an outgrowth of the Automatic Synthesis Program, has the following improvements: more versatile programming language; more convenient input/output format; some new subprograms which consolidate certain groups of statements that are often repeated; and variable dimensioning. The pertinent difference between the two programs is that VASP has variable dimensioning and more efficient storage. The documentation for the VASP program contains a VASP dictionary and example problems. The dictionary contains a description of each subroutine and instructions on its use. The example problems include dynamic response, optimal control gain, solution of the sampled data matrix Riccati equation, matrix decomposition, and a pseudo-inverse of a matrix. This program is written in FORTRAN IV and has been implemented on the IBM 360. The VASP program was developed in 1971.

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

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

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

Anatomical study of the pelvis in patients with adolescent idiopathic scoliosis

PubMed Central

Qiu, Xu-Sheng; Zhang, Jun-Jie; Yang, Shang-Wen; Lv, Feng; Wang, Zhi-Wei; Chiew, Jonathan; Ma, Wei-Wei; Qiu, Yong

2012-01-01

Standing posterior–anterior (PA) radiographs from our clinical practice show that the concave and convex ilia are not always symmetrical in patients with adolescent idiopathic scoliosis (AIS). Transverse pelvic rotation may explain this observation, or pelvic asymmetry may be responsible. The present study investigated pelvic symmetry by examining the volume and linear measurements of the two hipbones in patients with AIS. Forty-two female patients with AIS were recruited for the study. Standing PA radiographs (covering the thoracic and lumbar spinal regions and the entire pelvis), CT scans and 3D reconstructions of the pelvis were obtained for all subjects. The concave/convex ratio of the inferior ilium at the sacroiliac joint medially (SI) and the anterior superior iliac spine laterally (ASIS) were measured on PA radiographs. Hipbone volumes and several distortion and abduction parameters were measured by post-processing software. The concave/convex ratio of SI–ASIS on PA radiographs was 0.97, which was significantly < 1 (P < 0.001). The concave and convex hipbone volumes were comparable in patients with AIS. The hipbone volumes were 257.3 ± 43.5 cm3 and 256.9 ± 42.6 cm3 at the concave and convex sides, respectively (P > 0.05). Furthermore, all distortion and abduction parameters were comparable between the convex and concave sides. Therefore, the present study showed that there was no pelvic asymmetry in patients with AIS, although the concave/convex ratio of SI–ASIS on PA radiographs was significantly < 1. The clinical phenomenon of asymmetrical concave and convex ilia in patients with AIS in preoperative standing PA radiographs may be caused by transverse pelvic rotation, but it is not due to developmental asymmetry or distortion of the pelvis. PMID:22133294

Anatomical study of the pelvis in patients with adolescent idiopathic scoliosis.

PubMed

Qiu, Xu-Sheng; Zhang, Jun-Jie; Yang, Shang-Wen; Lv, Feng; Wang, Zhi-Wei; Chiew, Jonathan; Ma, Wei-Wei; Qiu, Yong

2012-02-01

Standing posterior-anterior (PA) radiographs from our clinical practice show that the concave and convex ilia are not always symmetrical in patients with adolescent idiopathic scoliosis (AIS). Transverse pelvic rotation may explain this observation, or pelvic asymmetry may be responsible. The present study investigated pelvic symmetry by examining the volume and linear measurements of the two hipbones in patients with AIS. Forty-two female patients with AIS were recruited for the study. Standing PA radiographs (covering the thoracic and lumbar spinal regions and the entire pelvis), CT scans and 3D reconstructions of the pelvis were obtained for all subjects. The concave/convex ratio of the inferior ilium at the sacroiliac joint medially (SI) and the anterior superior iliac spine laterally (ASIS) were measured on PA radiographs. Hipbone volumes and several distortion and abduction parameters were measured by post-processing software. The concave/convex ratio of SI-ASIS on PA radiographs was 0.97, which was significantly < 1 (P < 0.001). The concave and convex hipbone volumes were comparable in patients with AIS. The hipbone volumes were 257.3 ± 43.5 cm(3) and 256.9 ± 42.6 cm(3) at the concave and convex sides, respectively (P > 0.05). Furthermore, all distortion and abduction parameters were comparable between the convex and concave sides. Therefore, the present study showed that there was no pelvic asymmetry in patients with AIS, although the concave/convex ratio of SI-ASIS on PA radiographs was significantly < 1. The clinical phenomenon of asymmetrical concave and convex ilia in patients with AIS in preoperative standing PA radiographs may be caused by transverse pelvic rotation, but it is not due to developmental asymmetry or distortion of the pelvis. © 2011 The Authors. Journal of Anatomy © 2011 Anatomical Society.

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

Congruency effects in dot comparison tasks: convex hull is more important than dot area.

PubMed

Gilmore, Camilla; Cragg, Lucy; Hogan, Grace; Inglis, Matthew

2016-11-16

The dot comparison task, in which participants select the more numerous of two dot arrays, has become the predominant method of assessing Approximate Number System (ANS) acuity. Creation of the dot arrays requires the manipulation of visual characteristics, such as dot size and convex hull. For the task to provide a valid measure of ANS acuity, participants must ignore these characteristics and respond on the basis of number. Here, we report two experiments that explore the influence of dot area and convex hull on participants' accuracy on dot comparison tasks. We found that individuals' ability to ignore dot area information increases with age and display time. However, the influence of convex hull information remains stable across development and with additional time. This suggests that convex hull information is more difficult to inhibit when making judgements about numerosity and therefore it is crucial to control this when creating dot comparison tasks.

Space ultra-vacuum facility and method of operation

NASA Technical Reports Server (NTRS)

Naumann, Robert J. (Inventor)

1988-01-01

A wake shield space processing facility (10) for maintaining ultra-high levels of vacuum is described. The wake shield (12) is a truncated hemispherical section having a convex side (14) and a concave side (24). Material samples (68) to be processed are located on the convex side of the shield, which faces in the wake direction in operation in orbit. Necessary processing fixtures (20) and (22) are also located on the convex side. Support equipment including power supplies (40, 42), CMG package (46) and electronic control package (44) are located on the convex side (24) of the shield facing the ram direction. Prior to operation in orbit the wake shield is oriented in reverse with the convex side facing the ram direction to provide cleaning by exposure to ambient atomic oxygen. The shield is then baked-out by being pointed directed at the sun to obtain heating for a suitable period.

Portfolio optimization using fuzzy linear programming

NASA Astrophysics Data System (ADS)

Pandit, Purnima K.

2013-09-01

Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

Automation of reverse engineering process in aircraft modeling and related optimization problems

NASA Technical Reports Server (NTRS)

Li, W.; Swetits, J.

1994-01-01

During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for quadratic programming problems.

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.

High-Speed Numeric Function Generator Using Piecewise Quadratic Approximations

DTIC Science & Technology

2007-09-01

application; User specifies the fuction to approxiamte. % % This programs turns the function provided into an inline function... PRIMARY = < primary file 1> < primary file 2> #SECONDARY = <secondary file 1> <secondary file 2> #CHIP2 = <file to compile to user chip

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.

Natural-Scene Statistics Predict How the Figure–Ground Cue of Convexity Affects Human Depth Perception

PubMed Central

Fowlkes, Charless C.; Banks, Martin S.

2010-01-01

The shape of the contour separating two regions strongly influences judgments of which region is “figure” and which is “ground.” Convexity and other figure–ground cues are generally assumed to indicate only which region is nearer, but nothing about how much the regions are separated in depth. To determine the depth information conveyed by convexity, we examined natural scenes and found that depth steps across surfaces with convex silhouettes are likely to be larger than steps across surfaces with concave silhouettes. In a psychophysical experiment, we found that humans exploit this correlation. For a given binocular disparity, observers perceived more depth when the near surface's silhouette was convex rather than concave. We estimated the depth distributions observers used in making those judgments: they were similar to the natural-scene distributions. Our findings show that convexity should be reclassified as a metric depth cue. They also suggest that the dichotomy between metric and nonmetric depth cues is false and that the depth information provided many cues should be evaluated with respect to natural-scene statistics. Finally, the findings provide an explanation for why figure–ground cues modulate the responses of disparity-sensitive cells in visual cortex. PMID:20505093

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

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

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

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

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.

Development of Quadratic Programming Algorithm Based on Interior Point Method with Estimation Mechanism of Active Constraints

NASA Astrophysics Data System (ADS)

Hashimoto, Hiroyuki; Takaguchi, Yusuke; Nakamura, Shizuka

Instability of calculation process and increase of calculation time caused by increasing size of continuous optimization problem remain the major issues to be solved to apply the technique to practical industrial systems. This paper proposes an enhanced quadratic programming algorithm based on interior point method mainly for improvement of calculation stability. The proposed method has dynamic estimation mechanism of active constraints on variables, which fixes the variables getting closer to the upper/lower limit on them and afterwards releases the fixed ones as needed during the optimization process. It is considered as algorithm-level integration of the solution strategy of active-set method into the interior point method framework. We describe some numerical results on commonly-used bench-mark problems called “CUTEr” to show the effectiveness of the proposed method. Furthermore, the test results on large-sized ELD problem (Economic Load Dispatching problems in electric power supply scheduling) are also described as a practical industrial application.

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Statistical estimation via convex optimization for trending and performance monitoring

NASA Astrophysics Data System (ADS)

Samar, Sikandar

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

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.

Retrospective Cost Adaptive Control with Concurrent Closed-Loop Identification

NASA Astrophysics Data System (ADS)

Sobolic, Frantisek M.

Retrospective cost adaptive control (RCAC) is a discrete-time direct adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC is known to work on systems given minimal modeling information which is the leading numerator coefficient and any nonminimum-phase (NMP) zeros of the plant transfer function. This information is normally needed a priori and is key in the development of the filter, also known as the target model, within the retrospective performance variable. A novel approach to alleviate the need for prior modeling of both the leading coefficient of the plant transfer function as well as any NMP zeros is developed. The extension to the RCAC algorithm is the use of concurrent optimization of both the target model and the controller coefficients. Concurrent optimization of the target model and controller coefficients is a quadratic optimization problem in the target model and controller coefficients separately. However, this optimization problem is not convex as a joint function of both variables, and therefore nonconvex optimization methods are needed. Finally, insights within RCAC that include intercalated injection between the controller numerator and the denominator, unveil the workings of RCAC fitting a specific closed-loop transfer function to the target model. We exploit this interpretation by investigating several closed-loop identification architectures in order to extract this information for use in the target model.

Optimization of Culture Conditions for Enrichment of Saccharomyces cerevisiae with Dl-α-Tocopherol by Response Surface Methodology.

PubMed

Mohajeri Amiri, Morteza; Fazeli, Mohammad Reza; Amini, Mohsen; Hayati Roodbari, Nasim; Samadi, Nasrin

2017-01-01

Designing enriched probiotic supplements may have some advantages including protection of probiotic microorganism from oxidative destruction, improving enzyme activity of the gastrointestinal tract, and probably increasing half-life of micronutrient. In this study Saccharomyces cerevisiae enriched with dl-α-tocopherol was produced as an accumulator and transporter of a lipid soluble vitamin for the first time. By using one variable at the time screening studies, three independent variables were selected. Optimization of the level of dl-α-tocopherol entrapment in S. cerevisiae cells was performed by using Box-Behnken design via design expert software. A modified quadratic polynomial model appropriately fit the data. The convex shape of three-dimensional plots reveal that we could calculate the optimal point of the response in the range of parameters. The optimum points of independent parameters to maximize the response were dl-α-tocopherol initial concentration of 7625.82 µg/mL, sucrose concentration of 6.86 % w/v, and shaking speed of 137.70 rpm. Under these conditions, the maximum level of dl-α-tocopherol in dry cell weight of S. cerevisiae was 5.74 µg/g. The resemblance between the R-squared and adjusted R-squared and acceptable value of C.V% revealed acceptability and accuracy of the model.

Accelerated Edge-Preserving Image Restoration Without Boundary Artifacts

PubMed Central

Matakos, Antonios; Ramani, Sathish; Fessler, Jeffrey A.

2013-01-01

To reduce blur in noisy images, regularized image restoration methods have been proposed that use non-quadratic regularizers (like l1 regularization or total-variation) that suppress noise while preserving edges in the image. Most of these methods assume a circulant blur (periodic convolution with a blurring kernel) that can lead to wraparound artifacts along the boundaries of the image due to the implied periodicity of the circulant model. Using a non-circulant model could prevent these artifacts at the cost of increased computational complexity. In this work we propose to use a circulant blur model combined with a masking operator that prevents wraparound artifacts. The resulting model is non-circulant, so we propose an efficient algorithm using variable splitting and augmented Lagrangian (AL) strategies. Our variable splitting scheme, when combined with the AL framework and alternating minimization, leads to simple linear systems that can be solved non-iteratively using FFTs, eliminating the need for more expensive CG-type solvers. The proposed method can also efficiently tackle a variety of convex regularizers including edge-preserving (e.g., total-variation) and sparsity promoting (e.g., l1 norm) regularizers. Simulation results show fast convergence of the proposed method, along with improved image quality at the boundaries where the circulant model is inaccurate. PMID:23372080

Least-Squares Approximation of an Improper by a Proper Correlation Matrix Using a Semi-Infinite Convex Program. Research Report 87-7.

ERIC Educational Resources Information Center

Knol, Dirk L.; ten Berge, Jos M. F.

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977). It is shown that the minimization problem…

Manual for automatic generation of finite element models of spiral bevel gears in mesh

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Reddy, S.; Kumar, A.

1994-01-01

The goal of this research is to develop computer programs that generate finite element models suitable for doing 3D contact analysis of faced milled spiral bevel gears in mesh. A pinion tooth and a gear tooth are created and put in mesh. There are two programs: Points.f and Pat.f to perform the analysis. Points.f is based on the equation of meshing for spiral bevel gears. It uses machine tool settings to solve for an N x M mesh of points on the four surfaces, pinion concave and convex, and gear concave and convex. Points.f creates the file POINTS.OUT, an ASCI file containing N x M points for each surface. (N is the number of node points along the length of the tooth, and M is nodes along the height.) Pat.f reads POINTS.OUT and creates the file tl.out. Tl.out is a series of PATRAN input commands. In addition to the mesh density on the tooth face, additional user specified variables are the number of finite elements through the thickness, and the number of finite elements along the tooth full fillet. A full fillet is assumed to exist for both the pinion and gear.

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.

Asymmetric Bulkheads for Cylindrical Pressure Vessels

NASA Technical Reports Server (NTRS)

Ford, Donald B.

2007-01-01

Asymmetric bulkheads are proposed for the ends of vertically oriented cylindrical pressure vessels. These bulkheads, which would feature both convex and concave contours, would offer advantages over purely convex, purely concave, and flat bulkheads (see figure). Intended originally to be applied to large tanks that hold propellant liquids for launching spacecraft, the asymmetric-bulkhead concept may also be attractive for terrestrial pressure vessels for which there are requirements to maximize volumetric and mass efficiencies. A description of the relative advantages and disadvantages of prior symmetric bulkhead configurations is prerequisite to understanding the advantages of the proposed asymmetric configuration: In order to obtain adequate strength, flat bulkheads must be made thicker, relative to concave and convex bulkheads; the difference in thickness is such that, other things being equal, pressure vessels with flat bulkheads must be made heavier than ones with concave or convex bulkheads. Convex bulkhead designs increase overall tank lengths, thereby necessitating additional supporting structure for keeping tanks vertical. Concave bulkhead configurations increase tank lengths and detract from volumetric efficiency, even though they do not necessitate additional supporting structure. The shape of a bulkhead affects the proportion of residual fluid in a tank that is, the portion of fluid that unavoidably remains in the tank during outflow and hence cannot be used. In this regard, a flat bulkhead is disadvantageous in two respects: (1) It lacks a single low point for optimum placement of an outlet and (2) a vortex that forms at the outlet during outflow prevents a relatively large amount of fluid from leaving the tank. A concave bulkhead also lacks a single low point for optimum placement of an outlet. Like purely concave and purely convex bulkhead configurations, the proposed asymmetric bulkhead configurations would be more mass-efficient than is the flat bulkhead configuration. In comparison with both purely convex and purely concave configurations, the proposed asymmetric configurations would offer greater volumetric efficiency. Relative to a purely convex bulkhead configuration, the corresponding asymmetric configuration would result in a shorter tank, thus demanding less supporting structure. An asymmetric configuration provides a low point for optimum location of a drain, and the convex shape at the drain location minimizes the amount of residual fluid.

Active Mirror Predictive and Requirements Verification Software (AMP-ReVS)

NASA Technical Reports Server (NTRS)

Basinger, Scott A.

2012-01-01

This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the software package can be used to verify that the underlying requirements have been met.

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

NASA Technical Reports Server (NTRS)

Kottapalli, Sesi; Leyland, Jane

2014-01-01

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

PubMed

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

Variational Quantum Tomography with Incomplete Information by Means of Semidefinite Programs

NASA Astrophysics Data System (ADS)

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

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

NOLIN: A nonlinear laminate analysis program

NASA Technical Reports Server (NTRS)

Kibler, J. J.

1975-01-01

A nonlinear, plane-stress, laminate analysis program, NOLIN, was developed which accounts for laminae nonlinearity under inplane shear and transverse extensional stress. The program determines the nonlinear stress-strain behavior of symmetric laminates subjected to any combination of inplane shear and biaxial extensional loadings. The program has the ability to treat different stress-strain behavior in tension and compression, and predicts laminate failure using any or all of maximum stress, maximum strain, and quadratic interaction failure criteria. A brief description of the program is presented including discussion of the flow of information and details of the input required. Sample problems and a complete listing of the program is also provided.

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].

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 Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

NASA Astrophysics Data System (ADS)

Sandhu, Amit

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

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

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

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

Skala, Vaclav

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

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

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

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

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

H∞ memory feedback control with input limitation minimization for offshore jacket platform stabilization

NASA Astrophysics Data System (ADS)

Yang, Jia Sheng

2018-06-01

In this paper, we investigate a H∞ memory controller with input limitation minimization (HMCIM) for offshore jacket platforms stabilization. The main objective of this study is to reduce the control consumption as well as protect the actuator when satisfying the requirement of the system performance. First, we introduce a dynamic model of offshore platform with low order main modes based on mode reduction method in numerical analysis. Then, based on H∞ control theory and matrix inequality techniques, we develop a novel H∞ memory controller with input limitation. Furthermore, a non-convex optimization model to minimize input energy consumption is proposed. Since it is difficult to solve this non-convex optimization model by optimization algorithm, we use a relaxation method with matrix operations to transform this non-convex optimization model to be a convex optimization model. Thus, it could be solved by a standard convex optimization solver in MATLAB or CPLEX. Finally, several numerical examples are given to validate the proposed models and methods.

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 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.

A STRICTLY CONTRACTIVE PEACEMAN–RACHFORD SPLITTING METHOD FOR CONVEX PROGRAMMING

PubMed Central

BINGSHENG, HE; LIU, HAN; WANG, ZHAORAN; YUAN, XIAOMING

2014-01-01

In this paper, we focus on the application of the Peaceman–Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas–Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its convergence, while it is always faster whenever it is convergent. We first illustrate that the reason for this difference is that the iterative sequence generated by DRSM is strictly contractive, while that generated by PRSM is only contractive with respect to the solution set of the model. With only the convexity assumption on the objective function of the model under consideration, the convergence of PRSM is not guaranteed. But for this case, we show that the first t iterations of PRSM still enable us to find an approximate solution with an accuracy of O(1/t). A worst-case O(1/t) convergence rate of PRSM in the ergodic sense is thus established under mild assumptions. After that, we suggest attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and thus propose a strictly contractive PRSM. A worst-case O(1/t) convergence rate of this strictly contractive PRSM in a nonergodic sense is established. We show the numerical efficiency of the strictly contractive PRSM by some applications in statistical learning and image processing. PMID:25620862

Mechanical and optical behavior of a tunable liquid lens using a variable cross section membrane: modeling results

NASA Astrophysics Data System (ADS)

Flores-Bustamante, Mario C.; Rosete-Aguilar, Martha; Calixto, Sergio

2016-03-01

A lens containing a liquid medium and having at least one elastic membrane as one of its components is known as an elastic membrane lens (EML). The elastic membrane may have a constant or variable thickness. The optical properties of the EML change by modifying the profile of its elastic membrane(s). The EML formed of elastic constant thickness membrane(s) have been studied extensively. However, EML information using elastic membrane of variable thickness is limited. In this work, we present simulation results of the mechanical and optical behavior of two EML with variable thickness membranes (convex-plane membranes). The profile of its surfaces were modified by liquid medium volume increases. The model of the convex-plane membranes, as well as the simulation of its mechanical behavior, were performed using Solidworks® software; and surface's points of the deformed elastic lens were obtained. Experimental stress-strain data, obtained from a silicone rubber simple tensile test, according to ASTM D638 norm, were used in the simulation. Algebraic expressions, (Schwarzschild formula, up to four deformation coefficients, in a cylindrical coordinate system (r, z)), of the meridional profiles of the first and second surfaces of the deformed convex-plane membranes, were obtained using the results from Solidworks® and a program in the software Mathematica®. The optical performance of the EML was obtained by simulation using the software OSLO® and the algebraic expressions obtained in Mathematica®.

CudaChain: an alternative algorithm for finding 2D convex hulls on the GPU.

PubMed

Mei, Gang

2016-01-01

This paper presents an alternative GPU-accelerated convex hull algorithm and a novel S orting-based P reprocessing A pproach (SPA) for planar point sets. The proposed convex hull algorithm termed as CudaChain consists of two stages: (1) two rounds of preprocessing performed on the GPU and (2) the finalization of calculating the expected convex hull on the CPU. Those interior points locating inside a quadrilateral formed by four extreme points are first discarded, and then the remaining points are distributed into several (typically four) sub regions. For each subset of points, they are first sorted in parallel; then the second round of discarding is performed using SPA; and finally a simple chain is formed for the current remaining points. A simple polygon can be easily generated by directly connecting all the chains in sub regions. The expected convex hull of the input points can be finally obtained by calculating the convex hull of the simple polygon. The library Thrust is utilized to realize the parallel sorting, reduction, and partitioning for better efficiency and simplicity. Experimental results show that: (1) SPA can very effectively detect and discard the interior points; and (2) CudaChain achieves 5×-6× speedups over the famous Qhull implementation for 20M points.

The Factorability of Quadratics: Motivation for More Techniques

ERIC Educational Resources Information Center

Bosse, Michael J.; Nandakumar, N. R.

2005-01-01

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

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.

Nonlinear Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Badavi, Forooz F.

1989-01-01

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

A Centered Projective Algorithm for Linear Programming

DTIC Science & Technology

1988-02-01

zx/l to (PA Karmarkar’s algorithm iterates this procedure. An alternative method, the so-called affine variant (first proposed by Dikin [6] in 1967...trajectories, II. Legendre transform coordinates . central trajectories," manuscripts, to appear in Transactions of the American [6] I.I. Dikin ...34Iterative solution of problems of linear and quadratic programming," Soviet Mathematics Dokladv 8 (1967), 674-675. [7] I.I. Dikin , "On the speed of an

Probability, Problem Solving, and "The Price is Right."

ERIC Educational Resources Information Center

Wood, Eric

1992-01-01

This article discusses the analysis of a decision-making process faced by contestants on the television game show "The Price is Right". The included analyses of the original and related problems concern pattern searching, inductive reasoning, quadratic functions, and graphing. Computer simulation programs in BASIC and tables of…

A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

DTIC Science & Technology

2015-04-29

can be converted to a quadratic unconstrained binary optimization ( QUBO ) problem that uses 0/1-valued variables, and so they are often used...Frontiers in Physics, 2:5 (12 Feb 2014). [7] “Programming with QUBOs ,” (instructional document) D-Wave: The Quantum Computing Company, 2013. [8

A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem

DTIC Science & Technology

1990-09-01

Electr6nica e Inform’itica Industrial E.T.S. Ingenieros Industriales Universidad Polit6cnica, Madrid Technical Report SOL 90-12 September 1990 -Y...MURRAY* AND FRANCISCO J. PRIETOt *Systems Optimization Laboratory Department of Operations Research Stanford University tDept. de Automitica, Ingenieria

Design of reinforced areas of concrete column using quadratic polynomials

NASA Astrophysics Data System (ADS)

Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

2017-11-01

Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

Computational Efficiency of the Simplex Embedding Method in Convex Nondifferentiable Optimization

NASA Astrophysics Data System (ADS)

Kolosnitsyn, A. V.

2018-02-01

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

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

Thermal Protection System with Staggered Joints

NASA Technical Reports Server (NTRS)

Simon, Xavier D. (Inventor); Robinson, Michael J. (Inventor); Andrews, Thomas L. (Inventor)

2014-01-01

The thermal protection system disclosed herein is suitable for use with a spacecraft such as a reentry module or vehicle, where the spacecraft has a convex surface to be protected. An embodiment of the thermal protection system includes a plurality of heat resistant panels, each having an outer surface configured for exposure to atmosphere, an inner surface opposite the outer surface and configured for attachment to the convex surface of the spacecraft, and a joint edge defined between the outer surface and the inner surface. The joint edges of adjacent ones of the heat resistant panels are configured to mate with each other to form staggered joints that run between the peak of the convex surface and the base section of the convex surface.

A fast adaptive convex hull algorithm on two-dimensional processor arrays with a reconfigurable BUS system

NASA Technical Reports Server (NTRS)

Olariu, S.; Schwing, J.; Zhang, J.

1991-01-01

A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n.

The concave cusp as a determiner of figure-ground.

PubMed

Stevens, K A; Brookes, A

1988-01-01

The tendency to interpret as figure, relative to background, those regions that are lighter, smaller, and, especially, more convex is well known. Wherever convex opaque objects abut or partially occlude one another in an image, the points of contact between the silhouettes form concave cusps, each indicating the local assignment of figure versus ground across the contour segments. It is proposed that this local geometric feature is a preattentive determiner of figure-ground perception and that it contributes to the previously observed tendency for convexity preference. Evidence is presented that figure-ground assignment can be determined solely on the basis of the concave cusp feature, and that the salience of the cusp derives from local geometry and not from adjacent contour convexity.

Water resources planning and management : A stochastic dual dynamic programming approach

NASA Astrophysics Data System (ADS)

Goor, Q.; Pinte, D.; Tilmant, A.

2008-12-01

Allocating water between different users and uses, including the environment, is one of the most challenging task facing water resources managers and has always been at the heart of Integrated Water Resources Management (IWRM). As water scarcity is expected to increase over time, allocation decisions among the different uses will have to be found taking into account the complex interactions between water and the economy. Hydro-economic optimization models can capture those interactions while prescribing efficient allocation policies. Many hydro-economic models found in the literature are formulated as large-scale non linear optimization problems (NLP), seeking to maximize net benefits from the system operation while meeting operational and/or institutional constraints, and describing the main hydrological processes. However, those models rarely incorporate the uncertainty inherent to the availability of water, essentially because of the computational difficulties associated stochastic formulations. The purpose of this presentation is to present a stochastic programming model that can identify economically efficient allocation policies in large-scale multipurpose multireservoir systems. The model is based on stochastic dual dynamic programming (SDDP), an extension of traditional SDP that is not affected by the curse of dimensionality. SDDP identify efficient allocation policies while considering the hydrologic uncertainty. The objective function includes the net benefits from the hydropower and irrigation sectors, as well as penalties for not meeting operational and/or institutional constraints. To be able to implement the efficient decomposition scheme that remove the computational burden, the one-stage SDDP problem has to be a linear program. Recent developments improve the representation of the non-linear and mildly non- convex hydropower function through a convex hull approximation of the true hydropower function. This model is illustrated on a cascade of 14 reservoirs on the Nile river basin.

Remodelling of the bovine placenta: Comprehensive morphological and histomorphological characterization at the late embryonic and early accelerated fetal growth stages.

PubMed

Estrella, Consuelo Amor S; Kind, Karen L; Derks, Anna; Xiang, Ruidong; Faulkner, Nicole; Mohrdick, Melina; Fitzsimmons, Carolyn; Kruk, Zbigniew; Grutzner, Frank; Roberts, Claire T; Hiendleder, Stefan

2017-07-01

Placental function impacts growth and development with lifelong consequences for performance and health. We provide novel insights into placental development in bovine, an important agricultural species and biomedical model. Concepti with defined genetics and sex were recovered from nulliparous dams managed under standardized conditions to study placental gross morphological and histomorphological parameters at the late embryo (Day48) and early accelerated fetal growth (Day153) stages. Placentome number increased 3-fold between Day48 and Day153. Placental barrier thickness was thinner, and volume of placental components, and surface areas and densities were higher at Day153 than Day48. We confirmed two placentome types, flat and convex. At Day48, there were more convex than flat placentomes, and convex placentomes had a lower proportion of maternal connective tissue (P < 0.01). However, this was reversed at Day153, where convex placentomes were lower in number and had greater volume of placental components (P < 0.01- P < 0.001) and greater surface area (P < 0.001) than flat placentomes. Importantly, embryo (r = 0.50) and fetal (r = 0.30) weight correlated with total number of convex but not flat placentomes. Extensive remodelling of the placenta increases capacity for nutrient exchange to support rapidly increasing embryo-fetal weight from Day48 to Day153. The cellular composition of convex placentomes, and exclusive relationships between convex placentome number and embryo-fetal weight, provide strong evidence for these placentomes as drivers of prenatal growth. The difference in proportion of maternal connective tissue between placentome types at Day48 suggests that this tissue plays a role in determining placentome shape, further highlighting the importance of early placental development. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

Single lens laser beam shaper

DOEpatents

Liu, Chuyu [Newport News, VA; Zhang, Shukui [Yorktown, VA

2011-10-04

A single lens bullet-shaped laser beam shaper capable of redistributing an arbitrary beam profile into any desired output profile comprising a unitary lens comprising: a convex front input surface defining a focal point and a flat output portion at the focal point; and b) a cylindrical core portion having a flat input surface coincident with the flat output portion of the first input portion at the focal point and a convex rear output surface remote from the convex front input surface.

ON THE STRUCTURE OF \\mathcal{H}_{n - 1}-ALMOST EVERYWHERE CONVEX HYPERSURFACES IN \\mathbf{R}^{n + 1}

NASA Astrophysics Data System (ADS)

Dmitriev, V. G.

1982-04-01

It is proved that a hypersurface f imbedded in \\mathbf{R}^{n + 1}, n \\geq 2, which is locally convex at all points except for a closed set E with (n - 1)-dimensional Hausdorff measure \\mathcal{K}_{n - 1}(E) = 0, and strictly convex near E is in fact locally convex everywhere. The author also gives various corollaries. In particular, let M be a complete two-dimensional Riemannian manifold of nonnegative curvature K and E \\subset M a closed subset for which \\mathcal{K}_1(E) = 0. Assume further that there exists a neighborhood U \\supset E such that K(x) > 0 for x \\in U \\setminus E, f \\colon M \\to \\mathbf{R}^3 is such that f\\big\\vert _{U \\setminus E} is an imbedding, and f\\big\\vert _{M \\setminus E} \\in C^{1, \\alpha}, \\alpha > 2/3. Then f(M) is a complete convex surface in \\mathbf{R}^3. This result is an generalization of results in the paper reviewed in MR 51 # 11374.Bibliography: 19 titles.

Turbulent boundary layers subjected to multiple curvatures and pressure gradients

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Promode R.; Ahmed, Anwar

1993-01-01

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompaying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Gortler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

Users manual for flight control design programs

NASA Technical Reports Server (NTRS)

Nalbandian, J. Y.

1975-01-01

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

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.

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.

EVALUATION OF A MEASUREMENT METHOD FOR FOREST VEGETATION IN A LARGE-SCALE ECOLOGICAL SURVEY

EPA Science Inventory

We evaluate a field method for determining species richness and canopy cover of vascular plants for the Forest Health Monitoring Program (FHM), an ecological survey of U.S. forests. Measurements are taken within 12 1-m2 quadrats on 1/15 ha plots in FHM. Species richness and cover...

Primal Barrier Methods for Linear Programming

DTIC Science & Technology

1989-06-01

A Theoretical Bound Concerning the difficulties introduced by an ill-conditioned H- 1, Dikin [Dik67] and Stewart [Stew87] show for a full-rank A...Dik67] I. I. Dikin (1967). Iterative solution of problems of linear and quadratic pro- gramming, Doklady Akademii Nauk SSSR, Tom 174, No. 4. [Fia79] A. V

Interior-Point Methods for Linear Programming: A Challenge to the Simplex Method

DTIC Science & Technology

1988-07-01

subsequently found that the method was first proposed by Dikin in 1967 [6]. Search directions are generated by the same system (5). Any hint of quadratic...1982). Inexact Newton methods, SIAM Journal on Numerical Analysis 19, 400-408. [6] I. I. Dikin (1967). Iterative solution of problems of linear and

Optimization of a bundle divertor for FED

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

Hively, L.M.; Rothe, K.E.; Minkoff, M.

1982-01-01

Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations.

Order-Constrained Solutions in K-Means Clustering: Even Better than Being Globally Optimal

ERIC Educational Resources Information Center

Steinley, Douglas; Hubert, Lawrence

2008-01-01

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that…

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

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

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.

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

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Numerical procedure to determine geometric view factors for surfaces occluded by cylinders

NASA Technical Reports Server (NTRS)

Sawyer, P. L.

1978-01-01

A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.

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.

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

NASA Technical Reports Server (NTRS)

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

2014-01-01

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

On the time-weighted quadratic sum of linear discrete systems

NASA Technical Reports Server (NTRS)

Jury, E. I.; Gutman, S.

1975-01-01

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-08-18

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

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

EPA Science Inventory

Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

Improved flight-simulator viewing lens

NASA Technical Reports Server (NTRS)

Kahlbaum, W. M.

1979-01-01

Triplet lens system uses two acrylic plastic double convex lenses and one polystyrene plastic single convex lens to reduce chromatic distortion and lateral aberation, especially at large field angles within in-line systems of flight simulators.

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.

Interface Shape Control Using Localized Heating during Bridgman Growth

NASA Technical Reports Server (NTRS)

Volz, M. P.; Mazuruk, K.; Aggarwal, M. D.; Croll, A.

2008-01-01

Numerical calculations were performed to assess the effect of localized radial heating on the melt-crystal interface shape during vertical Bridgman growth. System parameters examined include the ampoule, melt and crystal thermal conductivities, the magnitude and width of localized heating, and the latent heat of crystallization. Concave interface shapes, typical of semiconductor systems, could be flattened or made convex with localized heating. Although localized heating caused shallower thermal gradients ahead of the interface, the magnitude of the localized heating required for convexity was less than that which resulted in a thermal inversion ahead of the interface. A convex interface shape was most readily achieved with ampoules of lower thermal conductivity. Increasing melt convection tended to flatten the interface, but the amount of radial heating required to achieve a convex interface was essentially independent of the convection intensity.

Pin stack array for thermoacoustic energy conversion

DOEpatents

Keolian, Robert M.; Swift, Gregory W.

1995-01-01

A thermoacoustic stack for connecting two heat exchangers in a thermoacoustic energy converter provides a convex fluid-solid interface in a plane perpendicular to an axis for acoustic oscillation of fluid between the two heat exchangers. The convex surfaces increase the ratio of the fluid volume in the effective thermoacoustic volume that is displaced from the convex surface to the fluid volume that is adjacent the surface within which viscous energy losses occur. Increasing the volume ratio results in an increase in the ratio of transferred thermal energy to viscous energy losses, with a concomitant increase in operating efficiency of the thermoacoustic converter. The convex surfaces may be easily provided by a pin array having elements arranged parallel to the direction of acoustic oscillations and with effective radial dimensions much smaller than the thicknesses of the viscous energy loss and thermoacoustic energy transfer volumes.

Implications of a quadratic stream definition in radiative transfer theory.

NASA Technical Reports Server (NTRS)

Whitney, C.

1972-01-01

An explicit definition of the radiation-stream concept is stated and applied to approximate the integro-differential equation of radiative transfer with a set of twelve coupled differential equations. Computational efficiency is enhanced by distributing the corresponding streams in three-dimensional space in a totally symmetric way. Polarization is then incorporated in this model. A computer program based on the model is briefly compared with a Monte Carlo program for simulation of horizon scans of the earth's atmosphere. It is found to be considerably faster.

Idiopathic and normal lateral lumbar curves: muscle effects interpreted by 12th rib length asymmetry with pathomechanic implications for lumbar idiopathic scoliosis.

PubMed

Grivas, Theodoros B; Burwell, R Geoffrey; Kechagias, Vasileios; Mazioti, Christina; Fountas, Apostolos; Kolovou, Dimitra; Christodoulou, Evangelos

2016-01-01

The historical view of scoliosis as a primary rotation deformity led to debate about the pathomechanic role of paravertebral muscles; particularly multifidus, thought by some to be scoliogenic, counteracting, uncertain, or unimportant. Here, we address lateral lumbar curves (LLC) and suggest a pathomechanic role for quadrates lumborum, (QL) in the light of a new finding, namely of 12th rib bilateral length asymmetry associated with idiopathic and small non-scoliosis LLC. Group 1: The postero-anterior spinal radiographs of 14 children (girls 9, boys 5) aged 9-18, median age 13 years, with right lumbar idiopathic scoliosis (IS) and right LLC less that 10°, were studied. The mean Cobb angle was 12° (range 5-22°). Group 2: In 28 children (girls 17, boys 11) with straight spines, postero-anterior spinal radiographs were evaluated similarly to the children with the LLC, aged 8-17, median age 13 years. The ratio of the right/left 12th rib lengths and it's reliability was calculated. The difference of the ratio between the two groups was tested; and the correlation between the ratio and the Cobb angle estimated. Statistical analysis was done using the SPSS package. The ratio's reliability study showed intra-observer +/-0,036 and the inter-observer error +/-0,042 respectively in terms of 95 % confidence limit of the error of measurements. The 12th rib was longer on the side of the curve convexity in 12 children with LLC and equal in two patients with lumbar scoliosis. The 12th rib ratios of the children with lumbar curve were statistically significantly greater than in those with straight spines. The correlation of the 12th rib ratio with Cobb angle was statistically significant. The 12th thoracic vertebrae show no axial rotation (or minimal) in the LLC and no rotation in the straight spine group. It is not possible, at present, to determine whether the 12th convex rib lengthening is congenitally lengthened, induced mechanically, or both. Several small muscles are attached to the 12th ribs. We focus attention here on the largest of these muscles namely, QL. It has attachments to the pelvis, 12th ribs and transverse processes of lumbar vertebrae as origins and as insertions. Given increased muscle activity on the lumbar curve convexity and similar to the interpretations of earlier workers outlined above, we suggest two hypotheses, relatively increased activity of the right QL muscle causes the LLCs (first hypothesis); or counteracts the lumbar curvature as part of the body's attempt to compensate for the curvature (second hypothesis). These hypotheses may be tested by electrical stimulation studies of QL muscles in subjects with lumbar IS by revealing respectively curve worsening or correction. We suggest that one mechanism leading to relatively increased length of the right 12 ribs is mechanotransduction in accordance with Wolff's and Pauwels Laws.

PILA: Sub-Meter Localization Using CSI from Commodity Wi-Fi Devices

PubMed Central

Tian, Zengshan; Li, Ze; Zhou, Mu; Jin, Yue; Wu, Zipeng

2016-01-01

The aim of this paper is to present a new indoor localization approach by employing the Angle-of-arrival (AOA) and Received Signal Strength (RSS) measurements in Wi-Fi network. To achieve this goal, we first collect the Channel State Information (CSI) by using the commodity Wi-Fi devices with our designed three antennas to estimate the AOA of Wi-Fi signal. Second, we propose a direct path identification algorithm to obtain the direct signal path for the sake of reducing the interference of multipath effect on the AOA estimation. Third, we construct a new objective function to solve the localization problem by integrating the AOA and RSS information. Although the localization problem is non-convex, we use the Second-order Cone Programming (SOCP) relaxation approach to transform it into a convex problem. Finally, the effectiveness of our approach is verified based on the prototype implementation by using the commodity Wi-Fi devices. The experimental results show that our approach can achieve the median error 0.7 m in the actual indoor environment. PMID:27735879

PILA: Sub-Meter Localization Using CSI from Commodity Wi-Fi Devices.

PubMed

Tian, Zengshan; Li, Ze; Zhou, Mu; Jin, Yue; Wu, Zipeng

2016-10-10

The aim of this paper is to present a new indoor localization approach by employing the Angle-of-arrival (AOA) and Received Signal Strength (RSS) measurements in Wi-Fi network. To achieve this goal, we first collect the Channel State Information (CSI) by using the commodity Wi-Fi devices with our designed three antennas to estimate the AOA of Wi-Fi signal. Second, we propose a direct path identification algorithm to obtain the direct signal path for the sake of reducing the interference of multipath effect on the AOA estimation. Third, we construct a new objective function to solve the localization problem by integrating the AOA and RSS information. Although the localization problem is non-convex, we use the Second-order Cone Programming (SOCP) relaxation approach to transform it into a convex problem. Finally, the effectiveness of our approach is verified based on the prototype implementation by using the commodity Wi-Fi devices. The experimental results show that our approach can achieve the median error 0.7 m in the actual indoor environment.

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.

Shear thickening and jamming in suspensions of different particle shapes

NASA Astrophysics Data System (ADS)

Brown, Eric; Zhang, Hanjun; Forman, Nicole; Betts, Douglas; Desimone, Joseph; Maynor, Benjamin; Jaeger, Heinrich

2012-02-01

We investigated the role of particle shape on shear thickening and jamming in densely packed suspensions. Various particle shapes were fabricated including rods of different aspect ratios and non-convex hooked rods. A rheometer was used to measure shear stress vs. shear rate for a wide range of packing fractions for each shape. Each suspensions exhibits qualitatively similar Discontinuous Shear Thickening, in which the logarithmic slope of the stress vs. shear rate has the same scaling for each convex shape and diverges at a critical packing fraction φc. The value of φc varies with particle shape, and coincides with the onset of a yield stress, a.k.a. the jamming transition. This suggests the jamming transition controls shear thickening, and the only effect of particle shape on steady state bulk rheology of convex particles is a shift of φc. Intriguingly, viscosity curves for non-convex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. Qualitative shape dependence was only found in steady state rheology when the system was confined to small gaps where large aspect ratio particle are forced to order.

The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

PubMed Central

Araújo, Ricardo; Mateus, Octávio

2015-01-01

The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

Convex Curved Crystal Spectograph for Pulsed Plasma Sources.

DTIC Science & Technology

The geometry of a convex curved crystal spectrograph as applied to pulsed plasma sources is presented. Also presented are data from the dense plasma focus with particular emphasis on the absolute intensity of line radiations.

AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

NASA Technical Reports Server (NTRS)

Lehtinen, B.

1994-01-01

AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user with open-loop system information including stability, controllability, and observability. The AESOP program is written in FORTRAN IV for interactive execution and has been implemented on an IBM 3033 computer using TSS 370. As currently configured, AESOP has a central memory requirement of approximately 2 Megs of 8 bit bytes. Memory requirements can be reduced by redimensioning arrays in the AESOP program. Graphical output requires adaptation of the AESOP plot routines to whatever device is available. The AESOP program was developed in 1984.

Electrostatic stiffening and induced persistence length for coassembled molecular bottlebrushes

NASA Astrophysics Data System (ADS)

Storm, Ingeborg M.; Stuart, Martien A. Cohen; de Vries, Renko; Leermakers, Frans A. M.

2018-03-01

A self-consistent field analysis for tunable contributions to the persistence length of isolated semiflexible polymer chains including electrostatically driven coassembled deoxyribonucleic acid (DNA) bottlebrushes is presented. When a chain is charged, i.e., for polyelectrolytes, there is, in addition to an intrinsic rigidity, an electrostatic stiffening effect, because the electric double layer resists bending. For molecular bottlebrushes, there is an induced contribution due to the grafts. We explore cases beyond the classical phantom main-chain approximation and elaborate molecularly more realistic models where the backbone has a finite volume, which is necessary for treating coassembled bottlebrushes. We find that the way in which the linear charge density or the grafting density is regulated is important. Typically, the stiffening effect is reduced when there is freedom for these quantities to adapt to the curvature stresses. Electrostatically driven coassembled bottlebrushes, however, are relatively stiff because the chains have a low tendency to escape from the compressed regions and the electrostatic binding force is largest in the convex part. For coassembled bottlebrushes, the induced persistence length is a nonmonotonic function of the polymer concentration: For low polymer concentrations, the stiffening grows quadratically with coverage; for semidilute polymer concentrations, the brush chains retract and regain their Gaussian size. When doing so, they lose their induced persistence length contribution. Our results correlate well with observed physical characteristics of electrostatically driven coassembled DNA-bioengineered protein-polymer bottlebrushes.

Constraints on single-field inflation

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

Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico

2016-06-28

Many alternatives to canonical slow-roll inflation have been proposed over the years, one of the main motivations being to have a model, capable of generating observable values of non-Gaussianity. In this work, we (re-)explore the physical implications of a great majority of such models within a single, effective field theory framework (including novel models with large non-Gaussianity discussed for the first time below). The constraints we apply — both theoretical and experimental — are found to be rather robust, determined to a great extent by just three parameters: the coefficients of the quadratic EFT operators (δN){sup 2} and δNδE, andmore » the slow-roll parameter ε. This allows to significantly limit the majority of single-field alternatives to canonical slow-roll inflation. While the existing data still leaves some room for most of the considered models, the situation would change dramatically if the current upper limit on the tensor-to-scalar ratio decreased down to r<10{sup −2}. Apart from inflationary models driven by plateau-like potentials, the single-field model that would have a chance of surviving this bound is the recently proposed slow-roll inflation with weakly-broken galileon symmetry. In contrast to canonical slow-roll inflation, the latter model can support r<10{sup −2} even if driven by a convex potential, as well as generate observable values for the amplitude of non-Gaussianity.« less

Novel Discrete Element Method for 3D non-spherical granular particles.

NASA Astrophysics Data System (ADS)

Seelen, Luuk; Padding, Johan; Kuipers, Hans

2015-11-01

Granular materials are common in many industries and nature. The different properties from solid behavior to fluid like behavior are well known but less well understood. The main aim of our work is to develop a discrete element method (DEM) to simulate non-spherical granular particles. The non-spherical shape of particles is important, as it controls the behavior of the granular materials in many situations, such as static systems of packed particles. In such systems the packing fraction is determined by the particle shape. We developed a novel 3D discrete element method that simulates the particle-particle interactions for a wide variety of shapes. The model can simulate quadratic shapes such as spheres, ellipsoids, cylinders. More importantly, any convex polyhedron can be used as a granular particle shape. These polyhedrons are very well suited to represent non-rounded sand particles. The main difficulty of any non-spherical DEM is the determination of particle-particle overlap. Our model uses two iterative geometric algorithms to determine the overlap. The algorithms are robust and can also determine multiple contact points which can occur for these shapes. With this method we are able to study different applications such as the discharging of a hopper or silo. Another application the creation of a random close packing, to determine the solid volume fraction as a function of the particle shape.

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.

Compliant tactile sensor that delivers a force vector

NASA Technical Reports Server (NTRS)

Torres-Jara, Eduardo (Inventor)

2010-01-01

Tactile Sensor. The sensor includes a compliant convex surface disposed above a sensor array, the sensor array adapted to respond to deformation of the convex surface to generate a signal related to an applied force vector. The applied force vector has three components to establish the direction and magnitude of an applied force. The compliant convex surface defines a dome with a hollow interior and has a linear relation between displacement and load including a magnet disposed substantially at the center of the dome above a sensor array that responds to magnetic field intensity.

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).

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.

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

User's guide for the northern hardwood stand models: SIMSAP and SIMTIM

Treesearch

Dale S. Solomon; Richard A. Hosmer; Richard A. Hosmer

1987-01-01

SIMSAP and SlMTlM are computer programs that have been developed to simulate the stand growth and development of natural and treated evenaged northern hardwood stands. SIMSAP begins with species distributions by quality classes in sapling stands after regeneration. SIMTIM, the poletimber-sawtimber-harvest phase, uses stocking guides based on quadratic mean stand...

Measuring Human Performance on Clustering Problems: Some Potential Objective Criteria and Experimental Research Opportunities

ERIC Educational Resources Information Center

Brusco, Michael J.

2007-01-01

The study of human performance on discrete optimization problems has a considerable history that spans various disciplines. The two most widely studied problems are the Euclidean traveling salesperson problem and the quadratic assignment problem. The purpose of this paper is to outline a program of study for the measurement of human performance on…

Unsteady transonic flow analysis for low aspect ratio, pointed wings.

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Ruo, S. Y.; Wu, J. M.; Liu, D. Y.

1973-01-01

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.

Axial jet mixing of ethanol in cylindrical containers during weightlessness

NASA Technical Reports Server (NTRS)

Aydelott, J. C.

1979-01-01

An experimental program was conducted to examine the liquid flow patterns that result from the axial jet mixing of ethanol in 10-centimeter-diameter cylindrical tanks in weightlessness. A convex hemispherically ended tank and two Centaur liquid-hydrogen-tank models were used for the study. Four distinct liquid flow patterns were observed to be a function of the tank geometry, the liquid-jet velocity, the volume of liquid in the tank, and the location of the tube from which the liquid jet exited.

Integrating UniTree with the data migration API

NASA Technical Reports Server (NTRS)

Schrodel, David G.

1994-01-01

The Data Migration Application Programming Interface (DMAPI) has the potential to allow developers of open systems Hierarchical Storage Management (HSM) products to virtualize native file systems without the requirement to make changes to the underlying operating system. This paper describes advantages of virtualizing native file systems in hierarchical storage management systems, the DMAPI at a high level, what the goals are for the interface, and the integration of the Convex UniTree+HSM with DMAPI along with some of the benefits derived in the resulting product.

Collaborative Research: Further Developments in the Global Resolution of Convex Programs with Complementary Contraints

DTIC Science & Technology

2014-10-31

Grant Number FA9550-11-1-0260. †Air Force Office of Scientific Research Grant Number FA9550-11-1-0151. 1 Abstract We have developed methods for...Report 11/04/2014 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR)/ RTA Arlington, Virginia 22203 Air...Force Research Laboratory Air Force Materiel Command REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188 1. REPORT DATE (DD-MM-YYYY) 2. REPORT

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.

A search asymmetry reversed by figure-ground assignment.

PubMed

Humphreys, G W; Müller, H

2000-05-01

We report evidence demonstrating that a search asymmetry favoring concave over convex targets can be reversed by altering the figure-ground assignment of edges in shapes. Visual search for a concave target among convex distractors is faster than search for a convex target among concave distractors (a search asymmetry). By using shapes with ambiguous local figure-ground relations, we demonstrated that search can be efficient (with search slopes around 10 ms/item) or inefficient (with search slopes around 30-40 ms/item) with the same stimuli, depending on whether edges are assigned to concave or convex "figures." This assignment process can operate in a top-down manner, according to the task set. The results suggest that attention is allocated to spatial regions following the computation of figure-ground relations in parallel across the elements present. This computation can also be modulated by top-down processes.

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.

Clearance detector and method for motion and distance

DOEpatents

Xavier, Patrick G [Albuquerque, NM

2011-08-09

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

Anomalous dynamics triggered by a non-convex equation of state in relativistic flows

NASA Astrophysics Data System (ADS)

Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.

2018-05-01

The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.

Estimating population size with correlated sampling unit estimates

Treesearch

David C. Bowden; Gary C. White; Alan B. Franklin; Joseph L. Ganey

2003-01-01

Finite population sampling theory is useful in estimating total population size (abundance) from abundance estimates of each sampled unit (quadrat). We develop estimators that allow correlated quadrat abundance estimates, even for quadrats in different sampling strata. Correlated quadrat abundance estimates based on mark–recapture or distance sampling methods occur...

Quadratic soliton self-reflection at a quadratically nonlinear interface

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

Self-Replicating Quadratics

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

Display-wide influences on figure-ground perception: the case of symmetry.

PubMed

Mojica, Andrew J; Peterson, Mary A

2014-05-01

Past research has demonstrated that convex regions are increasingly likely to be perceived as figures as the number of alternating convex and concave regions in test displays increases. This region-number effect depends on both a small preexisting preference for convex over concave objects and the presence of scene characteristics (i.e., uniform fill) that allow the integration of the concave regions into a background object/surface. These factors work together to enable the percept of convex objects in front of a background. We investigated whether region-number effects generalize to another property, symmetry, whose effectiveness as a figure property has been debated. Observers reported which regions they perceived as figures in black-and-white displays with alternating symmetric/asymmetric regions. In Experiments 1 and 2, the displays had articulated outer borders that preserved the symmetry/asymmetry of the outermost regions. Region-number effects were not observed, although symmetric regions were perceived as figures more often than chance. We hypothesized that the articulated outer borders prevented fitting a background interpretation to the asymmetric regions. In Experiment 3, we used straight-edge framelike outer borders and observed region-number effects for symmetry equivalent to those observed for convexity. These results (1) show that display-wide information affects figure assignment at a border, (2) extend the evidence indicating that the ability to fit background as well as foreground interpretations is critical in figure assignment, (3) reveal that symmetry and convexity are equally effective figure cues and, (4) demonstrate that symmetry serves as a figural property only when it is close to fixation.

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

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

ERIC Educational Resources Information Center

Laine, A. D.

2015-01-01

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

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.

Compliant tactile sensor for generating a signal related to an applied force

NASA Technical Reports Server (NTRS)

Torres-Jara, Eduardo (Inventor)

2012-01-01

Tactile sensor. The sensor includes a compliant convex surface disposed above a sensor array, the sensor array adapted to respond to deformation of the convex surface to generate a signal related to an applied force vector.

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.

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

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.

The role of spinal concave–convex biases in the progression of idiopathic scoliosis

PubMed Central

Driscoll, Mark; Moreau, Alain; Villemure, Isabelle; Parent, Stefan

2009-01-01

Inadequate understanding of risk factors involved in the progression of idiopathic scoliosis restrains initial treatment to observation until the deformity shows signs of significant aggravation. The purpose of this analysis is to explore whether the concave–convex biases associated with scoliosis (local degeneration of the intervertebral discs, nucleus migration, and local increase in trabecular bone-mineral density of vertebral bodies) may be identified as progressive risk factors. Finite element models of a 26° right thoracic scoliotic spine were constructed based on experimental and clinical observations that included growth dynamics governed by mechanical stimulus. Stress distribution over the vertebral growth plates, progression of Cobb angles, and vertebral wedging were explored in models with and without the biases of concave–convex properties. The inclusion of the bias of concave–convex properties within the model both augmented the asymmetrical loading of the vertebral growth plates by up to 37% and further amplified the progression of Cobb angles and vertebral wedging by as much as 5.9° and 0.8°, respectively. Concave–convex biases are factors that influence the progression of scoliotic curves. Quantifying these parameters in a patient with scoliosis may further provide a better clinical assessment of the risk of progression. PMID:19130096

Organizing principles for dense packings of nonspherical hard particles: Not all shapes are created equal

NASA Astrophysics Data System (ADS)

Torquato, Salvatore; Jiao, Yang

2012-07-01

We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids and certain smoothly shaped convex nonspherical particles [Torquato and Jiao, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.81.041310 81, 041310 (2010)]. Here we generalize them in order to guide one to ascertain the densest packings of other convex nonspherical particles as well as concave shapes. Our generalized organizing principles are explicitly stated as four distinct propositions. All of our organizing principles are applied to and tested against the most comprehensive set of both convex and concave particle shapes examined to date, including Catalan solids, prisms, antiprisms, cylinders, dimers of spheres, and various concave polyhedra. We demonstrate that all of the densest known packings associated with this wide spectrum of nonspherical particles are consistent with our propositions. Among other applications, our general organizing principles enable us to construct analytically the densest known packings of certain convex nonspherical particles, including spherocylinders, “lens-shaped” particles, square pyramids, and rhombic pyramids. Moreover, we show how to apply these principles to infer the high-density equilibrium crystalline phases of hard convex and concave particles. We also discuss the unique packing attributes of maximally random jammed packings of nonspherical particles.

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

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.

FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 1: Summary report

NASA Technical Reports Server (NTRS)

Jordan, T. M.

1970-01-01

The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.

Dynamic Geometry Software and Tracing Tangents in the Context of the Mean Value Theorem: Technique and Theory Production

ERIC Educational Resources Information Center

Martínez-Hernández, Cesar; Ulloa-Azpeitia, Ricardo

2017-01-01

Based on the theoretical elements of the instrumental approach to tool use known as Task-Technique-Theory (Artigue, 2002), this paper analyses and discusses the performance of graduate students enrolled in a Teacher Training program. The latter performance relates to tracing tangent lines to the curve of a quadratic function in Dynamic Geometry…

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

PubMed

Sun, Shiliang; Xie, Xijiong

2016-09-01

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously

NASA Astrophysics Data System (ADS)

Long, Kai; Wang, Xuan; Gu, Xianguang

2017-09-01

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the load-carrying capabilities and the thermal insulation properties. The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.

Quadratic Optimisation with One Quadratic Equality Constraint

DTIC Science & Technology

2010-06-01

This report presents a theoretical framework for minimising a quadratic objective function subject to a quadratic equality constraint. The first part of the report gives a detailed algorithm which computes the global minimiser without calling special nonlinear optimisation solvers. The second part of the report shows how the developed theory can be applied to solve the time of arrival geolocation problem.

Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

NASA Astrophysics Data System (ADS)

Yates, L. A.; Jarvis, P. D.

2018-04-01

We analyze the structure of the family of quadratic superalgebras, introduced in Jarvis et al (2011 J. Phys. A: Math. Theor. 44 235205), for the quadratic deformations of N  =  1 space-time conformal supersymmetry. We characterize in particular the ‘zero-step’ modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of N  =  1 space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate all physical states (including the vacuum state), while at the same time, superpartners do not exist.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

An improved multiple linear regression and data analysis computer program package

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.

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

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.

Directional Convexity and Finite Optimality Conditions.

DTIC Science & Technology

1984-03-01

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

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

Framework to model neutral particle flux in convex high aspect ratio structures using one-dimensional radiosity

NASA Astrophysics Data System (ADS)

Manstetten, Paul; Filipovic, Lado; Hössinger, Andreas; Weinbub, Josef; Selberherr, Siegfried

2017-02-01

We present a computationally efficient framework to compute the neutral flux in high aspect ratio structures during three-dimensional plasma etching simulations. The framework is based on a one-dimensional radiosity approach and is applicable to simulations of convex rotationally symmetric holes and convex symmetric trenches with a constant cross-section. The framework is intended to replace the full three-dimensional simulation step required to calculate the neutral flux during plasma etching simulations. Especially for high aspect ratio structures, the computational effort, required to perform the full three-dimensional simulation of the neutral flux at the desired spatial resolution, conflicts with practical simulation time constraints. Our results are in agreement with those obtained by three-dimensional Monte Carlo based ray tracing simulations for various aspect ratios and convex geometries. With this framework we present a comprehensive analysis of the influence of the geometrical properties of high aspect ratio structures as well as of the particle sticking probability on the neutral particle flux.

Strain relaxation in convex-graded InxAl1-xAs (x = 0.05-0.79) metamorphic buffer layers grown by molecular beam epitaxy on GaAs(001)

NASA Astrophysics Data System (ADS)

Solov'ev, V. A.; Chernov, M. Yu; Baidakova, M. V.; Kirilenko, D. A.; Yagovkina, M. A.; Sitnikova, A. A.; Komissarova, T. A.; Kop'ev, P. S.; Ivanov, S. V.

2018-01-01

This paper presents a study of structural properties of InGaAs/InAlAs quantum well (QW) heterostructures with convex-graded InxAl1-xAs (x = 0.05-0.79) metamorphic buffer layers (MBLs) grown by molecular beam epitaxy on GaAs substrates. Mechanisms of elastic strain relaxation in the convex-graded MBLs were studied by the X-ray reciprocal space mapping combined with the data of spatially-resolved selected area electron diffraction implemented in a transmission electron microscope. The strain relaxation degree was approximated for the structures with different values of an In step-back. Strong contribution of the strain relaxation via lattice tilt in addition to the formation of the misfit dislocations has been observed for the convex-graded InAlAs MBL, which results in a reduced threading dislocation density in the QW region as compared to a linear-graded MBL.

Efficient Compressed Sensing Based MRI Reconstruction using Nonconvex Total Variation Penalties

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

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 .

Torsional deformity of apical vertebra in adolescent idiopathic scoliosis.

PubMed

Kotwicki, Tomasz; Napiontek, Marek

2002-01-01

CT scans of structural thoracic idiopathic scoliosis were reviewed in nine patients admitted to our department for scoliosis surgery. The apical vertebra scans were chosen and the following parameters were evaluated: 1) alpha angle formed by the axis of vertebra and the axis of spinous process 2) beta concave and beta convex angle between the spinous process and the left and right transverse process, respectively, 3) gamma concave and gamma convex angle between the axis of vertebra and the left and right transverse process, respectively, 4) the rotation angle to the sagittal plane. The constant deviation of the spinous process towards the convex side of the curve was observed. The vertebral body itself was distorted towards the concavity of the curve. The angle between the spinous process and the transverse process was smaller on the convex side of the curve. The torsional, intravertebral deformity of the apical vertebra was a factor acting in the direction opposite to the rotation, in the sense to reduce the deformity of the spine in idiopathic scoliosis.

An axial temperature profile curvature criterion for the engineering of convex crystal growth interfaces in Bridgman systems

NASA Astrophysics Data System (ADS)

Peterson, Jeffrey H.; Derby, Jeffrey J.

2017-06-01

A unifying idea is presented for the engineering of convex melt-solid interface shapes in Bridgman crystal growth systems. Previous approaches to interface control are discussed with particular attention paid to the idea of a "booster" heater. Proceeding from the idea that a booster heater promotes a converging heat flux geometry and from the energy conservation equation, we show that a convex interface shape will naturally result when the interface is located in regions of the furnace where the axial thermal profile exhibits negative curvature, i.e., where d2 T / dz2 < 0 . This criterion is effective in explaining prior literature results on interface control and promising for the evaluation of new furnace designs. We posit that the negative curvature criterion may be applicable to the characterization of growth systems via temperature measurements in an empty furnace, providing insight about the potential for achieving a convex interface shape, without growing a crystal or conducting simulations.

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.

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

PubMed Central

Brassey, Charlotte A.; Sellers, William I.

2014-01-01

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

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.

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons

PubMed Central

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2012-01-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π. PMID:24027379

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2013-08-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.

Impact of trailing edge shape on the wake and propulsive performance of pitching panels

NASA Astrophysics Data System (ADS)

Van Buren, T.; Floryan, D.; Brunner, D.; Senturk, U.; Smits, A. J.

2017-01-01

The effects of changing the trailing edge shape on the wake and propulsive performance of a pitching rigid panel are examined experimentally. The panel aspect ratio is AR=1 , and the trailing edges are symmetric chevron shapes with convex and concave orientations of varying degree. Concave trailing edges delay the natural vortex bending and compression of the wake, and the mean streamwise velocity field contains a single jet. Conversely, convex trailing edges promote wake compression and produce a quadfurcated wake with four jets. As the trailing edge shape changes from the most concave to the most convex, the thrust and efficiency increase significantly.

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.

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

NASA Technical Reports Server (NTRS)

Pinson, Robin; Lu, Ping

2015-01-01

This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

Relaxation in control systems of subdifferential type

NASA Astrophysics Data System (ADS)

Tolstonogov, A. A.

2006-02-01

In a separable Hilbert space we consider a control system with evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. The constraint on the control is given by a multivalued function with non-convex values that is lower semicontinuous with respect to the variable states. Along with the original system we consider the system in which the constraint on the control is the upper semicontinuous convex-valued regularization of the original constraint. We study relations between the solution sets of these systems. As an application we consider a control variational inequality. We give an example of a control system of parabolic type with an obstacle.

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

On the polarizability dyadics of electrically small, convex objects

NASA Astrophysics Data System (ADS)

Lakhtakia, Akhlesh

1993-11-01

This communication on the polarizability dyadics of electrically small objects of convex shapes has been prompted by a recent paper published by Sihvola and Lindell on the polarizability dyadic of an electrically gyrotropic sphere. A mini-review of recent work on polarizability dyadics is appended.

On new fractional Hermite-Hadamard type inequalities for n-time differentiable quasi-convex functions and P-functions

NASA Astrophysics Data System (ADS)

Set, Erhan; Özdemir, M. Emin; Alan, E. Aykan

2017-04-01

In this article, by using the Hölder's inequality and power mean inequality the authors establish several inequalities of Hermite-Hadamard type for n- time differentiable quasi-convex functions and P- functions involving Riemann-Liouville fractional integrals.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

L 1-2 minimization for exact and stable seismic attenuation compensation

NASA Astrophysics Data System (ADS)

Wang, Yufeng; Ma, Xiong; Zhou, Hui; Chen, Yangkang

2018-06-01

Frequency-dependent amplitude absorption and phase velocity dispersion are typically linked by the causality-imposed Kramers-Kronig relations, which inevitably degrade the quality of seismic data. Seismic attenuation compensation is an important processing approach for enhancing signal resolution and fidelity, which can be performed on either pre-stack or post-stack data so as to mitigate amplitude absorption and phase dispersion effects resulting from intrinsic anelasticity of subsurface media. Inversion-based compensation with L1 norm constraint, enlightened by the sparsity of the reflectivity series, enjoys better stability over traditional inverse Q filtering. However, constrained L1 minimization serving as the convex relaxation of the literal L0 sparsity count may not give the sparsest solution when the kernel matrix is severely ill conditioned. Recently, non-convex metric for compressed sensing has attracted considerable research interest. In this paper, we propose a nearly unbiased approximation of the vector sparsity, denoted as L1-2 minimization, for exact and stable seismic attenuation compensation. Non-convex penalty function of L1-2 norm can be decomposed into two convex subproblems via difference of convex algorithm, each subproblem can be solved efficiently by alternating direction method of multipliers. The superior performance of the proposed compensation scheme based on L1-2 metric over conventional L1 penalty is further demonstrated by both synthetic and field examples.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

PubMed

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

PubMed Central

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-01-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques. PMID:21552465

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

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

Mehrotra, Sanjay

2016-09-07

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

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

PubMed

Zheng, Wenming; Lin, Zhouchen; Wang, Haixian

2014-04-01

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

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

PubMed Central

Ong, Frank; Lustig, Michael

2016-01-01

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information. PMID:28450978

Lateral facial profile may reveal the risk for sleep disordered breathing in children--the PANIC-study.

PubMed

Ikävalko, Tiina; Närhi, Matti; Lakka, Timo; Myllykangas, Riitta; Tuomilehto, Henri; Vierola, Anu; Pahkala, Riitta

2015-01-01

To evaluate the lateral view photography of the face as a tool for assessing morphological properties (i.e. facial convexity) as a risk factor for sleep disordered breathing (SDB) in children and to test how reliably oral health and non-oral healthcare professionals can visually discern the lateral profile of the face from the photographs. The present study sample consisted of 382 children 6-8 years of age who were participants in the Physical Activity and Nutrition in Children (PANIC) Study. Sleep was assessed by a sleep questionnaire administered by the parents. SDB was defined as apnoeas, frequent or loud snoring or nocturnal mouth breathing observed by the parents. The facial convexity was assessed with three different methods. First, it was clinically evaluated by the reference orthodontist (T.I.). Second, lateral view photographs were taken to visually sub-divide the facial profile into convex, normal or concave. The photos were examined by a reference orthodontist and seven different healthcare professionals who work with children and also by a dental student. The inter- and intra-examiner consistencies were calculated by Kappa statistics. Three soft tissue landmarks of the facial profile, soft tissue Glabella (G`), Subnasale (Sn) and soft tissue Pogonion (Pg`) were digitally identified to analyze convexity of the face and the intra-examiner reproducibility of the reference orthodontist was determined by calculating intra-class correlation coefficients (ICCs). The third way to express the convexity of the face was to calculate the angle of facial convexity (G`-Sn-Pg`) and to group it into quintiles. For analysis the lowest quintile (≤164.2°) was set to represent the most convex facial profile. The prevalence of the SDB in children with the most convex profiles expressed with the lowest quintile of the angle G`-Sn-Pg` (≤164.2°) was almost 2-fold (14.5%) compared to those with normal profile (8.1%) (p = 0.084). The inter-examiner Kappa values between the reference orthodontist and the other examiners for visually assessing the facial profile with the photographs ranged from poor-to-moderate (0.000-0.579). The best Kappa values were achieved between the two orthodontists (0.579). The intra-examiner Kappa value of the reference orthodontist for assessing the profiles was 0.920, with the agreement of 93.3%. In the ICC and its 95% CI between the two digital measurements, the angles of convexity of the facial profile (G`-Sn-Pg`) of the reference orthodontist were 0.980 and 0.951-0.992. In addition to orthodontists, it would be advantageous if also other healthcare professionals could play a key role in identifying certain risk features for SDB. However, the present results indicate that, in order to recognize the morphological risk for SDB, one would need to be trained for the purpose and, as well, needs sufficient knowledge of the growth and development of the face.

Estimating the quadratic mean diameter of fine woody debris for forest type groups of the United States

Treesearch

Christopher W. Woodall; Vicente J. Monleon

2009-01-01

The Forest Inventory and Analysis program of the Forest Service, U.S. Department of Agriculture conducts a national inventory of fine woody debris (FWD); however, the sampling protocols involve tallying only the number of FWD pieces by size class that intersect a sampling transect with no measure of actual size. The line intersect estimator used with those samples...

A design procedure and handling quality criteria for lateral directional flight control systems

NASA Technical Reports Server (NTRS)

Stein, G.; Henke, A. H.

1972-01-01

A practical design procedure for aircraft augmentation systems is described based on quadratic optimal control technology and handling-quality-oriented cost functionals. The procedure is applied to the design of a lateral-directional control system for the F4C aircraft. The design criteria, design procedure, and final control system are validated with a program of formal pilot evaluation experiments.

Diffusion Maps and Geometric Harmonics for Automatic Target Recognition (ATR). Volume 2. Appendices

DTIC Science & Technology

2007-11-01

of the Perron - Frobenius theorem, it suffices to prove that the chain is irreducible and aperiodic. • The irreducibility is a mere consequence of the...of each atom; this is due to the linear programming constraint that the coefficients be nonnegative 4. Chen et al. [20, 21] describe two algorithms for...projection of x onto the convex cone spanned by Ψ(t) with the origin at the apex; we provide details on computing x̃(t) in Section 4.1.3. Let x̃ (t) H

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Certification trails and software design for testability

NASA Technical Reports Server (NTRS)

Sullivan, Gregory F.; Wilson, Dwight S.; Masson, Gerald M.

1993-01-01

Design techniques which may be applied to make program testing easier were investigated. Methods for modifying a program to generate additional data which we refer to as a certification trail are presented. This additional data is designed to allow the program output to be checked more quickly and effectively. Certification trails were described primarily from a theoretical perspective. A comprehensive attempt to assess experimentally the performance and overall value of the certification trail method is reported. The method was applied to nine fundamental, well-known algorithms for the following problems: convex hull, sorting, huffman tree, shortest path, closest pair, line segment intersection, longest increasing subsequence, skyline, and voronoi diagram. Run-time performance data for each of these problems is given, and selected problems are described in more detail. Our results indicate that there are many cases in which certification trails allow for significantly faster overall program execution time than a 2-version programming approach, and also give further evidence of the breadth of applicability of this method.

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

PIFCGT: A PIF autopilot design program for general aviation aircraft

NASA Technical Reports Server (NTRS)

Broussard, J. R.

1983-01-01

This report documents the PIFCGT computer program. In FORTRAN, PIFCGT is a computer design aid for determing Proportional-Integral-Filter (PIF) control laws for aircraft autopilots implemented with a Command Generator Tracker (CGT). The program uses Linear-Quadratic-Regulator synthesis algorithms to determine feedback gains, and includes software to solve the feedforward matrix equation which is useful in determining the command generator tracker feedforward gains. The program accepts aerodynamic stability derivatives and computes the corresponding aerodynamic linear model. The nine autopilot modes that can be designed include four maneuver modes (ROLL SEL, PITCH SEL, HDG SEL, ALT SEL), four final approach models (APR GS, APR LOCI, APR LOCR, APR LOCP), and a BETA HOLD mode. The program has been compiled and executed on a CDC computer.

Determinants of Paracentrotus lividus sea urchin recruitment under oligotrophic conditions: Implications for conservation management.

PubMed

Oliva, Silvia; Farina, Simone; Pinna, Stefania; Guala, Ivan; Agnetta, Davide; Ariotti, Pierre Antoine; Mura, Francesco; Ceccherelli, Giulia

2016-06-01

Sea urchins may deeply shape the structure of macrophyte-dominated communities and require the implementation of sustainable management strategies. In the Mediterranean, the identification of the major recruitment determinants of the keystone sea urchin species Paracentrotus lividus is required, so that source areas of the populations can be identified and exploitation or programmed harvesting can be spatially managed. In this study a collection of eight possible determinants, these encompassing both the biotic (larvae, adult sea urchins, fish, encrusting coralline algae, habitat type and spatial arrangement of habitats) and abiotic (substrate complexity and nutritional status) realms was considered at different spatial scales (site, area, transect and quadrat). Data from a survey including sites subject to different levels of human influence (i.e. from urbanized to protected areas), but all corresponding to an oligotrophic and low-populated region were fitted by means of a generalized linear mixed model. Despite the extensive sampling effort of benthic quadrats, an overall paucity of recruits was found, recruits being aggregated in a very small number of quadrats and in few areas. The analysis of data detected substrate complexity, and adult sea urchin and predatory fish abundances as the momentous determinants of Paracentrotus lividus recruitment. Possible mechanisms of influence are discussed beyond the implications of conservation management. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Design of cryogenic tanks for launch vehicles

NASA Technical Reports Server (NTRS)

Copper, Charles; Pilkey, Walter D.; Haviland, John K.

1990-01-01

During the period since January 1990, work was concentrated on the problem of the buckling of the structure of an ALS (advanced launch systems) tank during the boost phase. The primary problem was to analyze a proposed hat stringer made by superplastic forming, and to compare it with an integrally stiffened stringer design. A secondary objective was to determine whether structural rings having the identical section to the stringers will provide adequate support against overall buckling. All of the analytical work was carried out with the TESTBED program on the CONVEX computer, using PATRAN programs to create models. Analyses of skin/stringer combinations have shown that the proposed stringer design is an adequate substitute for the integrally stiffened stringer. Using a highly refined mesh to represent the corrugations in the vertical webs of the hat stringers, effective values were obtained for cross-sectional area, moment of inertia, centroid height, and torsional constant. Not only can these values be used for comparison with experimental values, but they can also be used for beams to replace the stringers and frames in analytical models of complete sections of tank. The same highly refined model was used to represent a section of skin reinforced by a stringer and a ring segment in the configuration of a cross. It was intended that this would provide a baseline buckling analysis representing a basic mode, however, the analysis proved to be beyond the scope of the CONVEX computer. One quarter of this model was analyzed, however, to provide information on buckling between the spot welds. Models of large sections of the tank structure were made, using beam elements to model the stringers and frames. In order to represent the stiffening effects of pressure, stresses and deflections under pressure should first be obtained, and then the buckling analysis should be made on the structure so deflected. So far, uncharacteristic deflections under pressure were obtained from the TESTBED program using two types of structural elements. Similar results were obtained using the ANSYS program on a mainframe computer, although two finite element programs on microcomputers have yielded realistic results.

Variation in Phenometric Lapse Rates in Pasture Resources across Four Rayons in Kyrgyzstan

NASA Astrophysics Data System (ADS)

Henebry, G. M.; Tomaszewska, M. A.; Kelgenbaeva, K.

2017-12-01

High elevation pasture resources form the foundation of agro-pastoralist livelihoods in Kyrgyzstan and elsewhere in montane Central Asia. We explore the temporal and the topographical variation in phenometric lapse rates (PLRs: the change in a phenometric as a function of elevation) across four rayons in two oblasts of the Kyrgyz Republic—Alay, At-Bashy, Chong Alay, and Naryn—with the aim of identifying and quantifying robust generic patterns in the PLRs. We evaluate two fundamental phenometrics derived from the downward convex quadratic model of land surface phenology that links the NDVI to accumulated growing degree-day (AGDD). The peak height (PH) is the maximum NDVI value obtained from the fitted model. The thermal time to peak (TTP) is the amount of AGDD required to reach the PH. We fitted sixteen years of Landsat NDVI data at 30 m spatial resolution to annual AGDD progressions derived from MODIS land surface temperature time series at 1 km spatial resolution, yielding maps for each phenometric. If the coefficient of determination was less than 0.5, then the model fit was deemed a failure. We classified the reliability of pasture resources into five classes based on the number of years of successful model fit: very persistent (14-16 y); persistent (11-13 y); marginal (7-10 y); occasional (4-6); and rare (1-3). We explore the interactive roles of elevation, slope, aspect, latitude, and rayon on the PLRs and pasture resource persistence to identify critical areas for resource management.

Linear response and correlation of a self-propelled particle in the presence of external fields

NASA Astrophysics Data System (ADS)

Caprini, Lorenzo; Marini Bettolo Marconi, Umberto; Vulpiani, Angelo

2018-03-01

We study the non-equilibrium properties of non interacting active Ornstein-Uhlenbeck particles (AOUP) subject to an external nonuniform field using a Fokker-Planck approach with a focus on the linear response and time-correlation functions. In particular, we compare different methods to compute these functions including the unified colored noise approximation (UCNA). The AOUP model, described by the position of the particle and the active force acting on it, is usually mapped into a Markovian process, describing the motion of a fictitious passive particle in terms of its position and velocity, where the effect of the activity is transferred into a position-dependent friction. We show that the form of the response function of the AOUP depends on whether we put the perturbation on the position and keep unperturbed the active force in the original variables or perturb the position and maintain unperturbed the velocity in the transformed variables. Indeed, as a result of the change of variables the perturbation on the position becomes a perturbation both on the position and on the fictitious velocity. We test these predictions by considering the response for three types of convex potentials: quadratic, quartic and double-well potential. Moreover, by comparing the response of the AOUP model with the corresponding response of the UCNA model we conclude that although the stationary properties are fairly well approximated by the UCNA, the non equilibrium properties are not, an effect which is not negligible when the persistence time is large.

A Three-Phase Microgrid Restoration Model Considering Unbalanced Operation of Distributed Generation

DOE PAGES

Wang, Zeyu; Wang, Jianhui; Chen, Chen

2016-12-07

Recent severe outages highlight the urgency of improving grid resiliency in the U.S. Microgrid formation schemes are proposed to restore critical loads after outages occur. Most distribution networks have unbalanced configurations that are not represented in sufficient detail by single-phase models. This study provides a microgrid formation plan that adopts a three-phase network model to represent unbalanced distribution networks. The problem formulation has a quadratic objective function with mixed-integer linear constraints. The three-phase network model enables us to examine the three-phase power outputs of distributed generators (DGs), preventing unbalanced operation that might trip DGs. Because the DG unbalanced operation constraintmore » is non-convex, an iterative process is presented that checks whether the unbalanced operation limits for DGs are satisfied after each iteration of optimization. We also develop a relatively conservative linear approximation on the unbalanced operation constraint to handle larger networks. Compared with the iterative solution process, the conservative linear approximation is able to accelerate the solution process at the cost of sacrificing optimality to a limited extent. Simulation in the IEEE 34 node and IEEE 123 test feeders indicate that the proposed method yields more practical microgrid formations results. In addition, this paper explores the coordinated operation of DGs and energy storage (ES) installations. The unbalanced three-phase outputs of ESs combined with the relatively balanced outputs of DGs could supply unbalanced loads. In conclusion, the case study also validates the DG-ES coordination.« less

A Three-Phase Microgrid Restoration Model Considering Unbalanced Operation of Distributed Generation

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

Wang, Zeyu; Wang, Jianhui; Chen, Chen

Recent severe outages highlight the urgency of improving grid resiliency in the U.S. Microgrid formation schemes are proposed to restore critical loads after outages occur. Most distribution networks have unbalanced configurations that are not represented in sufficient detail by single-phase models. This study provides a microgrid formation plan that adopts a three-phase network model to represent unbalanced distribution networks. The problem formulation has a quadratic objective function with mixed-integer linear constraints. The three-phase network model enables us to examine the three-phase power outputs of distributed generators (DGs), preventing unbalanced operation that might trip DGs. Because the DG unbalanced operation constraintmore » is non-convex, an iterative process is presented that checks whether the unbalanced operation limits for DGs are satisfied after each iteration of optimization. We also develop a relatively conservative linear approximation on the unbalanced operation constraint to handle larger networks. Compared with the iterative solution process, the conservative linear approximation is able to accelerate the solution process at the cost of sacrificing optimality to a limited extent. Simulation in the IEEE 34 node and IEEE 123 test feeders indicate that the proposed method yields more practical microgrid formations results. In addition, this paper explores the coordinated operation of DGs and energy storage (ES) installations. The unbalanced three-phase outputs of ESs combined with the relatively balanced outputs of DGs could supply unbalanced loads. In conclusion, the case study also validates the DG-ES coordination.« less

Expected value based fuzzy programming approach to solve integrated supplier selection and inventory control problem with fuzzy demand

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Sunarsih; Kartono

2018-01-01

In this paper, a mathematical model in quadratic programming with fuzzy parameter is proposed to determine the optimal strategy for integrated inventory control and supplier selection problem with fuzzy demand. To solve the corresponding optimization problem, we use the expected value based fuzzy programming. Numerical examples are performed to evaluate the model. From the results, the optimal amount of each product that have to be purchased from each supplier for each time period and the optimal amount of each product that have to be stored in the inventory for each time period were determined with minimum total cost and the inventory level was sufficiently closed to the reference level.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 2

NASA Technical Reports Server (NTRS)

1972-01-01

The QL module of the Performance Analysis and Design Synthesis (PADS) computer program is described. Execution of this module is initiated when and if subroutine PADSI calls subroutine GROPE. Subroutine GROPE controls the high level logical flow of the QL module. The purpose of the module is to determine a trajectory that satisfies the necessary variational conditions for optimal performance. The module achieves this by solving a nonlinear multi-point boundary value problem. The numerical method employed is described. It is an iterative technique that converges quadratically when it does converge. The three basic steps of the module are: (1) initialization, (2) iteration, and (3) culmination. For Volume 1 see N73-13199.

78 FR 68833 - Combined Notice of Filings #1

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-15

... DEPARTMENT OF ENERGY Federal Energy Regulatory Commission Combined Notice of Filings 1 Take notice... Wallingford--CONVEX Services CL&P Electric Rate Schedule FERC No. 583 to be effective 1/1/2014. Filed Date: 11... Company submits CMEEC--CONVEX Services First Revised Rate Schedule FERC No. 576 to be effective 1/1/2014...

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.

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.

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

PubMed

Al-Mulhem, M; Al-Maghrabi, T

1998-01-01

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

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.

Detection of longitudinal ulcer using roughness value for computer aided diagnosis of Crohn's disease

NASA Astrophysics Data System (ADS)

Oda, Masahiro; Kitasaka, Takayuki; Furukawa, Kazuhiro; Watanabe, Osamu; Ando, Takafumi; Goto, Hidemi; Mori, Kensaku

2011-03-01

The purpose of this paper is to present a new method to detect ulcers, which is one of the symptoms of Crohn's disease, from CT images. Crohn's disease is an inflammatory disease of the digestive tract. Crohn's disease commonly affects the small intestine. An optical or a capsule endoscope is used for small intestine examinations. However, these endoscopes cannot pass through intestinal stenosis parts in some cases. A CT image based diagnosis allows a physician to observe whole intestine even if intestinal stenosis exists. However, because of the complicated shape of the small and large intestines, understanding of shapes of the intestines and lesion positions are difficult in the CT image based diagnosis. Computer-aided diagnosis system for Crohn's disease having automated lesion detection is required for efficient diagnosis. We propose an automated method to detect ulcers from CT images. Longitudinal ulcers make rough surface of the small and large intestinal wall. The rough surface consists of combination of convex and concave parts on the intestinal wall. We detect convex and concave parts on the intestinal wall by a blob and an inverse-blob structure enhancement filters. A lot of convex and concave parts concentrate on roughed parts. We introduce a roughness value to differentiate convex and concave parts concentrated on the roughed parts from the other on the intestinal wall. The roughness value effectively reduces false positives of ulcer detection. Experimental results showed that the proposed method can detect convex and concave parts on the ulcers.

“Soft that molds the hard:” Geometric morphometry of lateral atlantoaxial joints focusing on the role of cartilage in changing the contour of bony articular surfaces

PubMed Central

Prasad, Prashant Kumar; Salunke, Pravin; Sahni, Daisy; Kalra, Parveen

2017-01-01

Purpose: The existing literature on lateral atlantoaxial joints is predominantly on bony facets and is unable to explain various C1-2 motions observed. Geometric morphometry of facets would help us in understanding the role of cartilages in C1-2 biomechanics/kinematics. Objective: Anthropometric measurements (bone and cartilage) of the atlantoaxial joint and to assess the role of cartilages in joint biomechanics. Materials and Methods: The authors studied 10 cadaveric atlantoaxial lateral joints with the articular cartilage in situ and after removing it, using three-dimensional laser scanner. The data were compared using geometric morphometry with emphasis on surface contours of articulating surfaces. Results: The bony inferior articular facet of atlas is concave in both sagittal and coronal plane. The bony superior articular facet of axis is convex in sagittal plane and is concave (laterally) and convex medially in the coronal plane. The bony articulating surfaces were nonconcordant. The articular cartilages of both C1 and C2 are biconvex in both planes and are thicker than the concavities of bony articulating surfaces. Conclusion: The biconvex structure of cartilage converts the surface morphology of C1-C2 bony facets from concave on concavo-convex to convex on convex. This reduces the contact point making the six degrees of freedom of motion possible and also makes the joint gyroscopic. PMID:29403249

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.

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Cheetah: Starspot modeling code

NASA Astrophysics Data System (ADS)

Walkowicz, Lucianne; Thomas, Michael; Finkestein, Adam

2014-12-01

Cheetah models starspots in photometric data (lightcurves) by calculating the modulation of a light curve due to starspots. The main parameters of the program are the linear and quadratic limb darkening coefficients, stellar inclination, spot locations and sizes, and the intensity ratio of the spots to the stellar photosphere. Cheetah uses uniform spot contrast and the minimum number of spots needed to produce a good fit and ignores bright regions for the sake of simplicity.

Controllability of semi-infinite rod heating by a point source

NASA Astrophysics Data System (ADS)

Khurshudyan, A.

2018-04-01

The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

A new numerical approach to solve Thomas-Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming.

PubMed

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid

2016-01-01

In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

NASA Technical Reports Server (NTRS)

Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin

2014-01-01

This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

NASA Astrophysics Data System (ADS)

Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

2017-10-01

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Effect of dental arch convexity and type of archwire on frictional forces.

PubMed

Fourie, Zacharias; Ozcan, Mutlu; Sandham, Andrew

2009-07-01

Friction measurements in orthodontics are often derived from models by using brackets placed on flat models with various straight wires. Dental arches are convex in some areas. The objectives of this study were to compare the frictional forces generated in conventional flat and convex dental arch setups, and to evaluate the effect of different archwires on friction in both dental arch models. Two stainless steel models were designed and manufactured simulating flat and convex maxillary right buccal dental arches. Five stainless steel brackets from the maxillary incisor to the second premolar (slot size, 0.22 in, Victory, 3M Unitek, Monrovia, Calif) and a first molar tube were aligned and clamped on the metal model at equal distances of 6 mm. Four kinds of orthodontic wires were tested: (1) A. J. Wilcock Australian wire (0.016 in, G&H Wire, Hannover, Germany); and (2) 0.016 x 0.022 in, (3) 0.018 x 0.022 in, and (4) 0.019 x 0.025 in (3M Unitek GmbH, Seefeld, Germany). Gray elastomeric modules (Power O 110, Ormco, Glendora, Calif) were used for ligation. Friction tests were performed in the wet state with artificial saliva lubrication and by pulling 5 mm of the whole length of the archwire. Six measurements were made from each bracket-wire combination, and each test was performed with new combinations of materials for both arch setups (n = 48, 6 per group) in a universal testing machine (crosshead speed: 20 mm/min). Significant effects of arch model (P = 0.0000) and wire types (P = 0.0000) were found. The interaction term between the tested factors was not significant (P = 0.1581) (2-way ANOVA and Tukey test). Convex models resulted in significantly higher frictional forces (1015-1653 g) than flat models (680-1270 g) (P <0.05). In the flat model, significantly lower frictional forces were obtained with wire types 1 (679 g) and 3 (1010 g) than with types 2 (1146 g) and 4 (1270 g) (P <0.05). In the convex model, the lowest friction was obtained with wire types 1 (1015 g) and 3 (1142 g) (P >0.05). Type 1 wire tended to create the least overall friction in both flat and convex dental arch simulation models.

Processing eutectics in space

NASA Technical Reports Server (NTRS)

Douglas, F. C.; Galasso, F. S.

1974-01-01

Experimental work is reported which was directed toward obtaining interface shape control while a numerical thermal analysis program was being made operational. An experimental system was developed in which the solid-liquid interface in a directionally solidified aluminum-nickel eutectic could be made either concave to the melt or convex to the melt. This experimental system provides control over the solid-liquid interface shape and can be used to study the effect of such control on the microstructure. The SINDA thermal analysis program, obtained from Marshall Space Flight Center, was used to evaluate experimental directional solidification systems for the aluminum-nickel and the aluminum-copper eutectics. This program was applied to a three-dimensional ingot, and was used to calculate the thermal profiles in axisymmetric heat flow. The results show that solid-liquid interface shape control can be attained with physically realizable thermal configurations and the magnitudes of the required thermal inputs were indicated.

Matching by linear programming and successive convexification.

PubMed

Jiang, Hao; Drew, Mark S; Li, Ze-Nian

2007-06-01

We present a novel convex programming scheme to solve matching problems, focusing on the challenging problem of matching in a large search range and with cluttered background. Matching is formulated as metric labeling with L1 regularization terms, for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation. The unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space. This greatly reduces the size of the searching space. A successive convexification scheme solves the labeling problem in a coarse to fine manner. Importantly, the original cost function is reconvexified at each stage, in the new focus region only, and the focus region is updated so as to refine the searching result. This makes the method well-suited for large label set matching. Experiments demonstrate successful applications of the proposed matching scheme in object detection, motion estimation, and tracking.

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.

Quadratic Damping

ERIC Educational Resources Information Center

Fay, Temple H.

2012-01-01

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Visualising the Roots of Quadratic Equations with Complex Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2014-01-01

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Simply Prairie Homepage

Science.gov Websites

Ed Home - Data Home PRAIRIE ADVOCATES Project - QUADRAT STUDY Project Answer research questions multi-state quadrat study. Bob Lootens, Fermilab Join us! Check out the Quadrat Study Project. Prairie study a prairie "expert" to facilitate your research student Internet access an e-mail address

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

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

Reflections From a Fresnel Lens

ERIC Educational Resources Information Center

Keeports, David

2005-01-01

Reflection of light by a convex Fresnel lens gives rise to two distinct images. A highly convex inverted real reflective image forms on the object side of the lens, while an upright virtual reflective image forms on the opposite side of the lens. I describe here a set of laser experiments performed upon a Fresnel lens. These experiments provide…

Influence of crucible support and radial heating on the interface shape during vertical Bridgman GaAs growth

NASA Astrophysics Data System (ADS)

Koai, K.; Sonnenberg, K.; Wenzl, H.

1994-03-01

Crucible assembly in a vertical Bridgman furnace is investigated by a numerical finite element model with the aim to obtain convex interfaces during the growth of GaAs crystals. During the growth stage of the conic section, a new funnel shaped crucible support has been found more effective than the concentric cylinders design similar to that patented by AT & T in promoting interface convexity. For the growth stages of the constant diameter section, the furnace profile can be effectively modulated by localized radial heating at the gradient zone. With these two features being introduced into a new furnace design, it is shown numerically that enhancement of interface convexity can be achieved using the presently available crucible materials.

[Objective accommodation parameters depending on accommodation task].

PubMed

Tarutta, E P; Tarasova, N A; Dolzhenko, O O

2011-01-01

62 myopic patients were examined to study objective accommodation parameters in different conditions of accommodation stimulus presenting (use of convex lenses). Objective accommodation response (OAR) was studied using binocular open-field autorefractometer in different conditions of stimulus presenting: complete myopia correction and adding of convex lenses with increasing power from +1.0 till +3.0 D. In 88,5% of children and adolescents showed significant decrease of OAR for 1,5-2,75D in 3.0D stimulus. Additional correction with convex lenses with increasing power leads to further reduce of accommodation response. As a result induced dynamic refraction in eye-lens system is lower than accommodation task. Only addition of +2,5D lense approximates it to required index of -3.0D.

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.

Laser backscattering analytical model of Doppler power spectra about rotating convex quadric bodies of revolution

NASA Astrophysics Data System (ADS)

Gong, YanJun; Wu, ZhenSen; Wang, MingJun; Cao, YunHua

2010-01-01

We propose an analytical model of Doppler power spectra in backscatter from arbitrary rough convex quadric bodies of revolution (whose lateral surface is a quadric) rotating around axes. In the global Cartesian coordinate system, the analytical model deduced is suitable for general convex quadric body of revolution. Based on this analytical model, the Doppler power spectra of cones, cylinders, paraboloids of revolution, and sphere-cones combination are proposed. We analyze numerically the influence of geometric parameters, aspect angle, wavelength and reflectance of rough surface of the objects on the broadened spectra because of the Doppler effect. This analytical solution may contribute to laser Doppler velocimetry, and remote sensing of ballistic missile that spin.

Safe Onboard Guidance and Control Under Probabilistic Uncertainty

NASA Technical Reports Server (NTRS)

Blackmore, Lars James

2011-01-01

An algorithm was developed that determines the fuel-optimal spacecraft guidance trajectory that takes into account uncertainty, in order to guarantee that mission safety constraints are satisfied with the required probability. The algorithm uses convex optimization to solve for the optimal trajectory. Convex optimization is amenable to onboard solution due to its excellent convergence properties. The algorithm is novel because, unlike prior approaches, it does not require time-consuming evaluation of multivariate probability densities. Instead, it uses a new mathematical bounding approach to ensure that probability constraints are satisfied, and it is shown that the resulting optimization is convex. Empirical results show that the approach is many orders of magnitude less conservative than existing set conversion techniques, for a small penalty in computation time.

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

Geometric quadratic stochastic operator on countable infinite set

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

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-02-03

In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

An Unexpected Influence on a Quadratic

ERIC Educational Resources Information Center

Davis, Jon D.

2013-01-01

Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

NASA Astrophysics Data System (ADS)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

USGS Publications Warehouse

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

MM Algorithms for Geometric and Signomial Programming

PubMed Central

Lange, Kenneth; Zhou, Hua

2013-01-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545

MM Algorithms for Geometric and Signomial Programming.

PubMed

Lange, Kenneth; Zhou, Hua

2014-02-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Multi-task feature selection in microarray data by binary integer programming.

PubMed

Lan, Liang; Vucetic, Slobodan

2013-12-20

A major challenge in microarray classification is that the number of features is typically orders of magnitude larger than the number of examples. In this paper, we propose a novel feature filter algorithm to select the feature subset with maximal discriminative power and minimal redundancy by solving a quadratic objective function with binary integer constraints. To improve the computational efficiency, the binary integer constraints are relaxed and a low-rank approximation to the quadratic term is applied. The proposed feature selection algorithm was extended to solve multi-task microarray classification problems. We compared the single-task version of the proposed feature selection algorithm with 9 existing feature selection methods on 4 benchmark microarray data sets. The empirical results show that the proposed method achieved the most accurate predictions overall. We also evaluated the multi-task version of the proposed algorithm on 8 multi-task microarray datasets. The multi-task feature selection algorithm resulted in significantly higher accuracy than when using the single-task feature selection methods.

Response surface modeling of acid activation of raw diatomite using in sunflower oil bleaching by: Box-Behnken experimental design.

PubMed

Larouci, M; Safa, M; Meddah, B; Aoues, A; Sonnet, P

2015-03-01

The optimum conditions for acid activation of diatomite for maximizing bleaching efficiency of the diatomite in sun flower oil treatment were studied. Box-Behnken experimental design combining with response surface modeling (RSM) and quadratic programming (QP) was employed to obtain the optimum conditions of three independent variables (acid concentration, activation time and solid to liquid) for acid activation of diatomite. The significance of independent variables and their interactions were tested by means of the analysis of variance (ANOVA) with 95 % confidence limits (α = 0.05). The optimum values of the selected variables were obtained by solving the quadratic regression model, as well as by analyzing the response surface contour plots. The experimental conditions at this global point were determined to be acid concentration = 8.963 N, activation time = 11.9878 h, and solid to liquid ratio = 221.2113 g/l, the corresponding bleaching efficiency was found to be about 99 %.

Broiler responses to increasing selenium supplementation using Zn-L-selenomethionine with special attention to breast myopathies.

PubMed

Cemin, H S; Vieira, S L; Stefanello, C; Kindlein, L; Ferreira, T Z; Fireman, A K

2018-05-01

A study was conducted to evaluate growth performance, carcass and breast yields, and the occurrence and severity of white striping (WS) and wooden breast (WB) myopathies of broilers fed diets supplemented with increasing dietary levels of an organic source of selenium (Zn-L-SeMet). Broilers were fed 6 treatments with 12 replications of 26 birds in a 4-phase feeding program from 1 to 42 days. Corn-soy-based diets were supplemented with 0, 0.2, 0.4, 0.6, 0.8, and 1.0 ppm of Zn-L-SeMet. At 42 d, 6 birds were randomly selected from each pen (n = 72) and processed for carcass and breast yields. Breast fillets were scored for WS and WB at 42 days. Increasing Zn-L-SeMet led to quadratic responses (P < 0.05) for FCR from 1 to 7 d, BWG from 22 to 35 d, and for both responses from 8 to 21 d and 36 to 42 d, as well as in the overall period of 42 days. Carcass and breast yields presented a quadratic improvement (P < 0.01) with increasing Zn-L-SeMet supplementation and Se requirements were estimated at 0.85 and 0.86 ppm, respectively. In the overall period, estimates of Se requirements were 0.64 ppm for BWG and 0.67 ppm for FCR. White striping and WB scores presented quadratic increases (P < 0.01), and maximum scores were observed at 0.68 and 0.67 ppm, respectively. Broilers fed diets formulated without Se supplementation had a higher percentage of normal fillets compared to other Se supplementation levels (quadratic, P < 0.05). In conclusion, increasing Se supplementation to reach maximum growth performance led to higher degrees of severity of WS and WB. Selenium requirements determined in the present study were significantly higher than the present commercial recommendations.

Design of a multiple kernel learning algorithm for LS-SVM by convex programming.

PubMed

Jian, Ling; Xia, Zhonghang; Liang, Xijun; Gao, Chuanhou

2011-06-01

As a kernel based method, the performance of least squares support vector machine (LS-SVM) depends on the selection of the kernel as well as the regularization parameter (Duan, Keerthi, & Poo, 2003). Cross-validation is efficient in selecting a single kernel and the regularization parameter; however, it suffers from heavy computational cost and is not flexible to deal with multiple kernels. In this paper, we address the issue of multiple kernel learning for LS-SVM by formulating it as semidefinite programming (SDP). Furthermore, we show that the regularization parameter can be optimized in a unified framework with the kernel, which leads to an automatic process for model selection. Extensive experimental validations are performed and analyzed. Copyright © 2011 Elsevier Ltd. All rights reserved.

Work cost of thermal operations in quantum thermodynamics

NASA Astrophysics Data System (ADS)

Renes, Joseph M.

2014-07-01

Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. (Int. J. Th. Phys. 39, 2717 (2000)), we formulate the cost in the useful work of transforming one resource state into another as a linear program of convex optimization. This approach is based on the characterization of thermal quasiorder given by Janzing et al. and later by Horodecki and Oppenheim (Nat. Comm. 4, 2059 (2013)). Both characterizations are related to an extended version of majorization studied by Ruch, Schranner and Seligman under the name mixing distance (J. Chem. Phys. 69, 386 (1978)).

A minimization method on the basis of embedding the feasible set and the epigraph

NASA Astrophysics Data System (ADS)

Zabotin, I. Ya; Shulgina, O. N.; Yarullin, R. S.

2016-11-01

We propose a conditional minimization method of the convex nonsmooth function which belongs to the class of cutting-plane methods. During constructing iteration points a feasible set and an epigraph of the objective function are approximated by the polyhedral sets. In this connection, auxiliary problems of constructing iteration points are linear programming problems. In optimization process there is some opportunity of updating sets which approximate the epigraph. These updates are performed by periodically dropping of cutting planes which form embedding sets. Convergence of the proposed method is proved, some realizations of the method are discussed.

Slope gradient and shape effects on soil profiles in the northern mountainous forests of Iran

NASA Astrophysics Data System (ADS)

Fazlollahi Mohammadi, M.; Jalali, S. G. H.; Kooch, Y.; Said-Pullicino, D.

2016-12-01

In order to evaluate the variability of the soil profiles at two shapes (concave and convex) and five positions (summit, shoulder, back slope, footslope and toeslope) of a slope, a study of a virgin area was made in a Beech stand of mountain forests, northern Iran. Across the slope positions, the soil profiles demonstrated significant changes due to topography for two shape slopes. The solum depth of the convex slope was higher than the concave one in all five positions, and it decreased from the summit to shoulder and increased from the mid to lower slope positions for both convex and concave slopes. The thin solum at the upper positions and concave slope demonstrated that pedogenetic development is least at upper slope positions and concave slope where leaching and biomass productivity are less than at lower slopes and concave slope. A large decrease in the thickness of O and A horizons from the summit to back slope was noted for both concave and convex slopes, but it increased from back slope toward down slope for both of them. The average thickness of B horizons increased from summit to down slopes in the case of the concave slope, but in the case of convex slope it decreased from summit to shoulder and afterwards it increased to the down slope. The thicknesses of the different horizons varied in part in the different positions and shape slopes because they had different plant species cover and soil features, which were related to topography.