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1

Formulating Cyber-Security as Convex Optimization Problems  

E-print Network

to defend, a problem often referred to as cyber situation aware- ness. Situation awareness [3] is a commonFormulating Cyber-Security as Convex Optimization Problems Kyriakos G. Vamvoudakis, Jo~ao P. Mission-centric cyber-security analysts require a complete overview and understanding of the state

Hespanha, João Pedro

2

Formulating Cyber-Security as Convex Optimization Problems  

E-print Network

aware- ness. Situation awareness [3] is a common feature of many cyber-security solu- tions but most the biggest threat and prioritize which services to defend, a problem often referred to as cyber situationFormulating Cyber-Security as Convex Optimization ProblemsÃ? Kyriakos G. Vamvoudakis1 , Jo~ao P

Vigna, Giovanni

3

Convex Formulations of Aggregate Network Air Traffic Flow Optimization Problems  

E-print Network

Control Center. I. INTRODUCTION Research on the steady increase in air traffic volume has triggeredConvex Formulations of Aggregate Network Air Traffic Flow Optimization Problems Daniel B. Work, Student Member, IEEE, Alexandre M. Bayen, Member, IEEE Abstract--The problem of regulating air traffic

4

A nonisolated optimal solution for special reverse convex programming problems  

NASA Astrophysics Data System (ADS)

In this paper, an efficient algorithm is proposed for globally solving special reverse convex programming problems with more than one reverse convex constraints. The proposed algorithm provides a nonisolated global optimal solution which is also stable under small perturbations of the constraints, and it turns out that such an optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and the numerical experiment is given to illustrate the feasibility of the presented algorithm.

Shen, Pei-Ping; Chen, Yong-Qiang; Ma, Yuan

2009-02-01

5

Lossless Convexification of a Class of Non-Convex Optimal Control Problems for Linear Systems  

E-print Network

Lossless Convexification of a Class of Non-Convex Optimal Control Problems for Linear Systems Behc¸et Ac¸ikmes¸e and Lars Blackmore Abstract-- We consider a class of finite time horizon optimal control-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove

Williams, Brian C.

6

On the Complexity of Optimization Problems for 3Dimensional Convex Polyhedra and Decision Trees \\Lambda  

E-print Network

On the Complexity of Optimization Problems for 3­Dimensional Convex Polyhedra and Decision Trees@cs.jhu.edu Abstract We show that several well­known optimization problems involving 3­dimensional convex polyhedra. Key words: Convex polyhedra, approximation, Steinitz's theorem, planar graphs, art gallery theorems

Goodrich, Michael T.

7

An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems  

Microsoft Academic Search

In multicriteria optimization, several objective functions have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multicriteria optimization problem, where the objective functions involved are arbitrary convex functions and the set of feasible points is convex. The method is based on generating warm-start points for an efficient interior-point algorithm, while the approximation

Jörg Fliege

2006-01-01

8

Generalization of Primal-Dual Interior-Point Methods to Convex Optimization Problems in Conic Form  

Microsoft Academic Search

.    We generalize primal—dual interior-point methods for linear programming (LP) problems to the convex optimization problems\\u000a in conic form. Previously, the most comprehensive theory of symmetric primal—dual interior-point algorithms was given by Nesterov\\u000a and Todd for feasible regions expressed as the intersection of a symmetric cone with an affine subspace. In our setting, we\\u000a allow an arbitrary convex cone

Levent Tunçel

2001-01-01

9

Stat 375 Project Proposal: Convex relaxations and belief propagation equivalence in combinatorial optimization problems  

E-print Network

For my project I will investigate the equivalence between convex programming relaxations and message passing algorithms on hard, combinatorial optimization problems. It has been shown that when the LP relaxations of such problems as weighted b-matchings [1], max weight matchings [2], and max-weight independent set [3] [4] are tight, then the max-product

Matt Kraning

2011-01-01

10

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

PubMed Central

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

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

2012-01-01

11

An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization  

E-print Network

An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization topology, the delay can be controlled by varying the sizes of transistors in the circuit. Here, the size of a transistor is measured in terms of its channel width, since the channel lengths in a digital circuit

Sapatnekar, Sachin

12

A Sequential Approximation Bound for Some Sample-Dependent Convex Optimization Problems with Applications in Learning  

Microsoft Academic Search

In this paper, we study a class of sample dependent convex optimization problems, and derive a general sequential approximation\\u000a bound for their solutions. This analysis is closely related to the regret bound framework in online learning. However we apply\\u000a it to batch learning algorithms instead of online stochastic gradient decent methods. Applications of this analysis in some\\u000a classification and regression

Tong Zhang

2001-01-01

13

The optimal solution of a non-convex state-dependent LQR problem and its applications.  

PubMed

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417

Xu, Xudan; Zhu, J Jim; Zhang, Ping

2014-01-01

14

The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications  

PubMed Central

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417

Xu, Xudan; Zhu, J. Jim; Zhang, Ping

2014-01-01

15

Conditional Gradient Sliding for Convex Optimization  

E-print Network

Oct 17, 2014 ... and strongly convex problems, while still maintaining the optimal O(1/?) bound on the ...... One possible remedy to this issue is to incorporate the randomized smoothing ...... Hence, we employed a trial-and-error method to fine tune the .... SIAM Journal on Control and Optimization, 18(5):473487, 1980.

2014-10-17

16

An algorithm for linearizing convex extremal problems  

SciTech Connect

This paper suggests a method of approximating the solution of minimization problems for convex functions of several variables under convex constraints is suggested. The main idea of this approach is the approximation of a convex function by a piecewise linear function, which results in replacing the problem of convex programming by a linear programming problem. To carry out such an approximation, the epigraph of a convex function is approximated by the projection of a polytope of greater dimension. In the first part of the paper, the problem is considered for functions of one variable. In this case, an algorithm for approximating the epigraph of a convex function by a polygon is presented, it is shown that this algorithm is optimal with respect to the number of vertices of the polygon, and exact bounds for this number are obtained. After this, using an induction procedure, the algorithm is generalized to certain classes of functions of several variables. Applying the suggested method, polynomial algorithms for an approximate calculation of the L{sub p}-norm of a matrix and of the minimum of the entropy function on a polytope are obtained. Bibliography: 19 titles.

Gorskaya, Elena S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2010-06-09

17

Solution to Non-convex Electric Power Dispatch Problem Using Seeker Optimization Algorithm  

NASA Astrophysics Data System (ADS)

This paper presents the application of Seeker Optimization Algorithm (SOA) to constrained economic load dispatch problem. Independent simulations were performed over separate systems with different number of generating units having constraints like prohibited operating zones and ramp rate limits. The performance is also compared with other existing similar approaches. The proposed methodology was found to be robust, fast converging and more proficient over other existing techniques.

Krishnanand, K. R.; Rout, P. K.; Panigrahi, B. K.; Mohapatra, Ankita

18

A New Adaptive Algorithm for Convex Quadratic Multicriteria Optimization  

E-print Network

the prob- lem of solving one single-criteria convex-quadratic optimization problem by an interior-point method used for this problem. 1 Introduction Multicriteria optimization problems are a class of difficult The Interior-Point Algorithm 2.1 The Problem Let there be given a primal quadratic optimization problem (PQP

Fliege, Jörg

19

Support set expansion sensitivity analysis in convex quadratic optimization  

Microsoft Academic Search

In support set expansion sensitivity analysis, one concerns to find the range of parameter variation where the perturbed problem has an optimal solution with the support set that includes the support set of the given optimal solution of the unperturbed problem. In this article, we consider the perturbed convex quadratic optimization problem and present a method to identify the support

Kamal Mirnia; Alireza Ghaffari Hadigheh

2007-01-01

20

Sparse recovery via convex optimization  

NASA Astrophysics Data System (ADS)

This thesis considers the problem of estimating a sparse signal from a few (possibly noisy) linear measurements. In other words, we have y = Ax + z where A is a measurement matrix with more columns than rows, x is a sparse signal to be estimated, z is a noise vector, and y is a vector of measurements. This setup arises frequently in many problems ranging from MRI imaging to genomics to compressed sensing.We begin by relating our setup to an error correction problem over the reals, where a received encoded message is corrupted by a few arbitrary errors, as well as smaller dense errors. We show that under suitable conditions on the encoding matrix and on the number of arbitrary errors, one is able to accurately recover the message.We next show that we are able to achieve oracle optimality for x, up to a log factor and a factor of sqrt{s}, when we require the matrix A to obey an incoherence property. The incoherence property is novel in that it allows the coherence of A to be as large as O(1/ log n) and still allows sparsities as large as O(m/log n). This is in contrast to other existing results involving coherence where the coherence can only be as large as O(1/sqrt{m}) to allow sparsities as large as O(sqrt{m}). We also do not make the common assumption that the matrix A obeys a restricted eigenvalue condition.We then show that we can recover a (non-sparse) signal from a few linear measurements when the signal has an exactly sparse representation in an overcomplete dictionary. We again only require that the dictionary obey an incoherence property.Finally, we introduce the method of l_1 analysis and show that it is guaranteed to give good recovery of a signal from a few measurements, when the signal can be well represented in a dictionary. We require that the combined measurement/dictionary matrix satisfies a uniform uncertainty principle and we compare our results with the more standard l_1 synthesis approach.All our methods involve solving an l_1 minimization program which can be written as either a linear program or a second-order cone program, and the well-established machinery of convex optimization used to solve it rapidly.

Randall, Paige Alicia

21

A tutorial on convex optimization II: duality and interior point methods  

Microsoft Academic Search

In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to its ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to continue the overview of modern convex optimization from where our ACC2004 Tutorial on Convex Optimization left off, to cover important topics that were omitted

Haitham Hindi

2006-01-01

22

Large-Scale Convex Optimization via Saddle Point Computation  

Microsoft Academic Search

This article proposes large-scale convex optimization problems to be solved via saddlepoints of the standard Lagrangian. A recent approach for saddle point computation isspecialized, by way of a specific perturbation technique and unique scaling method, toconvex optimization problems with differentiable objective and constraint functions. Ineach iteration the update directions for primal and dual variables are determined by gradientsof the Lagrangian.

Markku Kallio; Charles H. Rosa

1994-01-01

23

On Equilibrium Pricing as Convex Optimization Jiawei Zhang  

E-print Network

optimization by an interior-point algorithm in polynomial time. 1 Introduction The study of competitive economy problem, and it could be computed by the Ellipsoid method or by efficient interior-point methods of these constraints yield equilibrium prices. Thus, finding a Fisher equilibrium becomes solving a convex optimization

Ye, Yinyu

24

Convex Optimization, Game Theory, and Variational Inequality Theory  

Microsoft Academic Search

In this article, we have provided a unified view of some basic theoretical foundations and main techniques in convex optimization, game theory, and VI theory. We put special emphasis on the generality of the VI framework, showing how it allows to tackle several interesting problems in nonlinear analysis, classical optimization, and equilibrium programming. In particular, we showed the relevance of

Gesualdo Scutari; Daniel P. Palomar; Francisco Facchinei; Jong-Shi Pang

2010-01-01

25

Robust boosting via convex optimization  

NASA Astrophysics Data System (ADS)

In this work we consider statistical learning problems. A learning machine aims to extract information from a set of training examples such that it is able to predict the associated label on unseen examples. We consider the case where the resulting classification or regression rule is a combination of simple rules - also called base hypotheses. The so-called boosting algorithms iteratively find a weighted linear combination of base hypotheses that predict well on unseen data. We address the following issues: o The statistical learning theory framework for analyzing boosting methods. We study learning theoretic guarantees on the prediction performance on unseen examples. Recently, large margin classification techniques emerged as a practical result of the theory of generalization, in particular Boosting and Support Vector Machines. A large margin implies a good generalization performance. Hence, we analyze how large the margins in boosting are and find an improved algorithm that is able to generate the maximum margin solution. o How can boosting methods be related to mathematical optimization techniques? To analyze the properties of the resulting classification or regression rule, it is of high importance to understand whether and under which conditions boosting converges. We show that boosting can be used to solve large scale constrained optimization problems, whose solutions are well characterizable. To show this, we relate boosting methods to methods known from mathematical optimization, and derive convergence guarantees for a quite general family of boosting algorithms. o How to make Boosting noise robust? One of the problems of current boosting techniques is that they are sensitive to noise in the training sample. In order to make boosting robust, we transfer the soft margin idea from support vector learning to boosting. We develop theoretically motivated regularized algorithms that exhibit a high noise robustness. o How to adapt boosting to regression problems? Boosting methods are originally designed for classification problems. To extend the boosting idea to regression problems, we use the previous convergence results and relations to semi-infinite programming to design boosting-like algorithms for regression problems. We show that these leveraging algorithms have desirable theoretical and practical properties. o Can boosting techniques be useful in practice? The presented theoretical results are guided by simulation results either to illustrate properties of the proposed algorithms or to show that they work well in practice. We report on successful applications in a non-intrusive power monitoring system, chaotic time series analysis and a drug discovery process. --- Anmerkung: Der Autor ist Träger des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2001/2002. In dieser Arbeit werden statistische Lernprobleme betrachtet. Lernmaschinen extrahieren Informationen aus einer gegebenen Menge von Trainingsmustern, so daß sie in der Lage sind, Eigenschaften von bisher ungesehenen Mustern - z.B. eine Klassenzugehörigkeit - vorherzusagen. Wir betrachten den Fall, bei dem die resultierende Klassifikations- oder Regressionsregel aus einfachen Regeln - den Basishypothesen - zusammengesetzt ist. Die sogenannten Boosting Algorithmen erzeugen iterativ eine gewichtete Summe von Basishypothesen, die gut auf ungesehenen Mustern vorhersagen. Die Arbeit behandelt folgende Sachverhalte: o Die zur Analyse von Boosting-Methoden geeignete Statistische Lerntheorie. Wir studieren lerntheoretische Garantien zur Abschätzung der Vorhersagequalität auf ungesehenen Mustern. Kürzlich haben sich sogenannte Klassifikationstechniken mit großem Margin als ein praktisches Ergebnis dieser Theorie herausgestellt - insbesondere Boosting und Support-Vektor-Maschinen. Ein großer Margin impliziert eine hohe Vorhersagequalität der Entscheidungsregel. Deshalb wird analysiert, wie groß der Margin bei Boosting ist und ein verbesserter Algorithmus vorgeschl

Rätsch, Gunnar

2001-12-01

26

August 2000 (Convex Optimization ) JP Goux The mega title ...  

E-print Network

A new class of proximal interior-point methods for optimization under positivity constraints (Convex Optimization ) ..... Roman Polyak Lagrangian ... Stephen Vavasis Convex relaxation for finding planted influential nodes in a social network

27

First and second order convex approximation strategies in structural optimization  

NASA Technical Reports Server (NTRS)

In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.

Fleury, C.

1989-01-01

28

From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation  

SciTech Connect

We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.

Egozcue, J. [ETS d'Enginyers de Camins, Canals i Ports, Gran Capita, s/n, 08034 Barcelona (Spain)], E-mail: juanjose.egozcue@upc.es; Meziat, R. [ETI Telecomunicaciones, Universidad de Castilla-La Mancha, 16071 Cuenca (Spain) and Departamento de Matematicas, Universidad de los Andes, Carrera 1, N 18A-10 Bogota (Colombia)], E-mail: rmeziat@uniandes.edu.co; Pedregal, P. [ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: pablo.pedregal@uclm.es

2002-12-19

29

Exploiting convexity in array antenna synthesis problems  

Microsoft Academic Search

Many efforts have been done in recent years to solve array antenna synthesis problems in a way as effective as possible. Stochastic optimization schemes have been widely applied, but useful mathematical properties of the problem, which may be useful in the synthesis process, have been neglected in many cases of interest. In this communication we show that in a number

O. M. Bucci; M. D'Urso; T. Isernia

2008-01-01

30

A randomized scheme for speeding up algorithms for linear and convex programming problems with high constraints-to-variables ratio  

Microsoft Academic Search

We extend Clarkson's randomized algorithm for linear programming to a general scheme for solving convex optimization problems. The scheme can be used to speed up existing algorithms on problems which have many more constraints than variables. In particular, we give a randomized algorithm for solving convex quadratic and linear programs, which uses that scheme together with a variant of Karmarkar's

Ilan Adler; Ron Shamir

1993-01-01

31

Kernel regression for travel time estimation via convex optimization  

E-print Network

Kernel regression for travel time estimation via convex optimization Sébastien Blandin , Laurent El Ghaoui and Alexandre Bayen Abstract--We develop an algorithm aimed at estimating travel time on segments of a road network using a convex optimiza- tion framework. Sampled travel time from probe vehicles

32

accuracy certificates for computational problems with convex structure  

E-print Network

whether x ? intX, and if it is not the case, returns a separator – a vector e such that. ?e, y? perspective, convex optimization techniques, like polynomial time interior point methods. (ipm's) for ...... Russian and East European. Math.

2008-11-26

33

Computational experience with a primal-dual interior point method for smooth convex placement problems  

Microsoft Academic Search

We present a primal-dual interior point method (IPM) for solving smooth convex optimization problems which arise during the placement of integrated circuits. The interior point method represents a substantial enhancement in flexibility versus other methods while having similar computational requirements. We illustrate that iterative solvers are efficient for calculation of search directions during optimization. Computational results are presented on a

Andrew Kennings; Mark Frazer; Anthony Vannelli

1998-01-01

34

6.253 Convex Analysis and Optimization, Spring 2010  

E-print Network

This course will focus on fundamental subjects in (deterministic) optimization, connected through the themes of convexity, geometric multipliers, and duality. The aim is to develop the core analytical and computational ...

Bertsekas, Dimitri

35

Stochastic Convex Optimization Shai Shalev-Shwartz  

E-print Network

- ent is strong convexity and regularization. Our results demonstrate that the celebrated theo- rem prediction setting where z = (x, y) is an instance-label pair, W is a subset of a Hilbert space, and f(w; x

Srebro, Nathan

36

Design of FIR pulse-shaping filter: Superiority of Differential Evolution optimization over Convex optimization  

Microsoft Academic Search

Design of different types of digital FIR filter is of paramount significance in various Digital Signal Processing (DSP) applications. Different optimization techniques can judiciously be utilized to determine the impulse response coefficients of such a filter. These optimization techniques may include some conventional processes such as Convex or Non-convex optimization methods or some evolutionary algorithms such as Genetic Algorithm (GA),

S. Chattopadhyay; S. K. Sanyal; A. Chandra

2010-01-01

37

Extension of primal-dual interior point methods to diff-convex problems on symmetric cones  

Microsoft Academic Search

We consider the extension of primal dual interior point methods for linear programming on symmetric cones, to a wider class of problems that includes approximate necessary optimality conditions for functions expressible as the difference of two convex functions of a special form. Our analysis applies the Jordan-algebraic approach to symmetric cones. As the basic method is local, we apply the

Tuomo Valkonen

2011-01-01

38

Maximum entropy and feasibility methods for convex and nonconvex inverse problems  

Microsoft Academic Search

We discuss informally two approaches to solving convex and nonconvex feasibility problems – via entropy optimization and via algebraic iterative methods. We shall highlight the advantages and disadvantages of each and give various related applications and limiting examples. While some of the results are very classical, they are not as well-known to practitioners as they should be. A key role

Jonathan M. Borwein

2012-01-01

39

Optimal average cost manufacturing flow controllers: convexity and differentiability  

Microsoft Academic Search

The authors consider the control of a production facility consisting of a single workstation with multiple failure modes and part types using a continuous flow control model. Technical issues concerning the convexity and differentiability of the differential cost function are investigated. It is proven that under an optimal control policy the differential cost is C1 on attractive control switching boundaries

Michael H. Veatch; Michael C. Caramanis

1999-01-01

40

Computational Experience with a New Class of Convex Underestimators: Box-constrained NLP Problems  

Microsoft Academic Search

In Akrotirianakis and Floudas (2004) we presented the theoretical foundations of a new class of convex underestimators for C2 nonconvex functions. In this paper, we present computational experience with those underestimators incorporated within a Branch-and-Bound algorithm for box-conatrained problems. The algorithm can be used to solve global optimization problems that involve C2 functions. We discuss several ways of incorporating the

Ioannis G. Akrotirianakis; Christodoulos A. Floudas

2004-01-01

41

QoS and Fairness Constrained Convex Optimization of Resource Allocation for Wireless Cellular and Ad Hoc Networks  

Microsoft Academic Search

For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations that allocate network resources to optimize SIR, maximize throughput and minimize de- lay. The distinguishing characteristics of these resource allocation formulations is that, by using convex optimization, they accommo- date a variety of realistic QoS and fairness constraints. Their glob- ally optimal solutions

David Julian; Mung Chiang; Daniel O'neill; Stephen P. Boyd

2002-01-01

42

A convex interior-point method for optimal OFDM PAR reduction  

Microsoft Academic Search

The main disadvantage of OFDM is the high time-domain peak-to-average power ratio (PAR) that limits transmitter power efficiency. This paper presents a convex optimization algorithm for minimizing the PAR of an OFDM signal subject to constraints on the constellation error vector magnitude (EVM). The derivation reduces computational complexity by exploiting known features of the optimization problem, such as OFDM's FFT

Alok Aggarwal; Teresa H. Meng

2005-01-01

43

MODERN CONVEX OPTIMIZATION Aharon Ben-Tal  

E-print Network

optimization programs one can solve well ("efficiently solv- able" programs) and when such a possibility is, not well posed!) "what are generic optimization programs we can solve well": #12;3 (!) As far as numerical.isye.gatech.edu/faculty-staff/profile.php?entry=an63 Fall Semester 2013 #12;2 Preface Mathematical Programming deals with optimization programs

Nemirovski, Arkadi

44

FIR Filter Design via Spectral Factorization and Convex Optimization  

Microsoft Academic Search

udio, spectrum shaping, ... ) upper bounds are convex in h; lower bounds are notMagnitude filter design problem involves magnitude specsClassical example: lowpass filter designlowpass filter with maximum stopband attenuation:521\\/51IS()l variables: h C R (filter coefficients),52 G R (stopband attenuation) parameters: 51 ( R (logarithmic passband ripple), n (order),Op (passband frequency), Os (stopband frequency)magnitude filter design problems are nonconvex can

Lieven Vandenberghe; Shao-po Wu; Stephen Boyd

1997-01-01

45

A partially inexact bundle method for convex semi-infinite minmax problems  

NASA Astrophysics Data System (ADS)

We present a bundle method for solving convex semi-infinite minmax problems which allows inexact solution of the inner maximization. The method is of the partially inexact oracle type, and it is aimed at reducing the occurrence of null steps and at improving bundle handling with respect to existing methods. Termination of the algorithm is proved at a point satisfying an approximate optimality criterion, and the results of some numerical experiments are also reported.

Fuduli, Antonio; Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna

2015-04-01

46

Selected Topics in Robust Convex Optimization  

E-print Network

tional chance constrained settings of problems with stochastic data, and (4) a ... Faculty of Industrial Engineering and Management, Technion – Israel Institute of .... first case, the uncertainty set is the direct product of uncertainty sets in the.

2006-09-12

47

Global and Convex Optimization in Modeling Environments ...  

E-print Network

Aug 12, 2002 ... This model is a frequently used classical GO test problem, originally due to ..... modeling and solution tips; and reviews a list of applications. .... Obviously, by taking, e.g., the Euclidean norm of the overall error in the model.

Administrator

2002-08-16

48

Stable sequential convex programming in a Hilbert space and its application for solving unstable problems  

NASA Astrophysics Data System (ADS)

A parametric convex programming problem with an operator equality constraint and a finite set of functional inequality constraints is considered in a Hilbert space. The instability of this problem and, as a consequence, the instability of the classical Lagrange principle for it is closely related to its regularity and the subdifferentiability properties of the value function in the optimization problem. A sequential Lagrange principle in nondifferential form is proved for the indicated convex programming problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. It is shown that the classical Lagrange principle in this problem can be naturally treated as a limiting variant of its stable sequential counterpart. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimal control problems and inverse problems is discussed. For two illustrative problems of these kinds, the corresponding stable Lagrange principles are formulated in sequential form.

Sumin, M. I.

2014-01-01

49

Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy optimization framework  

NASA Astrophysics Data System (ADS)

Radiation therapy is an important modality in treating various cancers. Various treatment planning and delivery technologies have emerged to support intensity modulated radiation therapy (IMRT), creating significant opportunities to advance this type of treatment. However, one of the fundamental questions in treatment planning and optimization, 'can we produce better treatment plans relying on the existing delivery technology?' still remains unanswered, in large part due to the underlying computational complexity of the problem, which, in turn, often stems from the optimization model being non-convex. We investigate the possibility of including the dose prescription, specified by the dose-volume histogram (DVH), within the convex optimization framework for inverse radiotherapy treatment planning. Specifically, we study the quality of approximating a given DVH with a superset of generalized equivalent uniform dose (gEUD)-based constraints, the so-called generalized moment constraints (GMCs). As a bi-product, we establish an analytic relationship between a DVH and a sequence of gEUD values. The newly proposed approach is promising as demonstrated by the computational study where the rectum DVH is considered. Unlike the precise partial-volume constraints formulation, which is commonly based on the mixed-integer model and necessitates the use of expensive computing resources to be solved to global optimality, our convex optimization approach is expected to be feasible for implementation on a conventional treatment planning station.

Zinchenko, Y.; Craig, T.; Keller, H.; Terlaky, T.; Sharpe, M.

2008-06-01

50

Studies integrating geometry, probability, and optimization under convexity  

E-print Network

Convexity has played a major role in a variety of fields over the past decades. Nevertheless, the convexity assumption continues to reveal new theoretical paradigms and applications. This dissertation explores convexity ...

Nogueira, Alexandre Belloni

2006-01-01

51

Solving convex programs by random walks  

Microsoft Academic Search

Minimizing a convex function over a convex set in n-dimensional space is a basic, general problem with many interesting special cases. Here, we present a simple new algorithm for convex optimization based on sampling by a random walk. It extends naturally to minimizing quasi-convex functions and to other generalizations.

Dimitris Bertsimas; Santosh Vempala

2004-01-01

52

Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging  

E-print Network

Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emissions as compared to CLEAN. With the advent of large radiotel...

Girard, Julien N; Starck, Jean Luc; Corbel, Stéphane; Woiselle, Arnaud; Tasse, Cyril; McKean, John P; Bobin, Jérôme

2015-01-01

53

Solving dynamic control problems via deterministic global optimization  

SciTech Connect

A significant multi-stage stochastic program from the area of financial planning is posed as a nonlinear stochastic control problem. The dynamic policy, called fixed-mix, results in a nonconvex optimization model. A deterministic global optimization algorithm specialized for this problem class produces a guaranteed optimal solution for realistic size applications. The proposed branch and bound type deterministic algorithm guarantees finite {element_of}-convergence to the global solution through the successive refinement of converging lower and upper bounds on the solution. These bounds are obtained through a novel convex lowering bounding and the subsequent solution of a series of nonlinear convex optimization problems. Computational results obtained with an efficient C implementation of the proposed procedure GLOFP, demonstrate the efficiency of the approach on a set of real world financial planning problems. These tests confirm that local optimization methods are prone to erroneously underestimate the efficient frontier. The concepts can be readily extended to other non-convex dynamic policies.

Mulvey, J.; Maranas, C.; Androulakis, I.P.; Floudas, C.; Berger, A.

1994-12-31

54

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

PubMed Central

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

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

55

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

PubMed

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

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

56

Efficient Market Making via Convex Optimization, and a Connection to Online Learning  

E-print Network

12 Efficient Market Making via Convex Optimization, and a Connection to Online Learning JACOB framework, we illustrate the mathematical parallels between cost-function-based markets and online learning. Efficient market making via convex optimization, and a connection to online learning. ACM Trans. Econ. Comp

Chen, Yiling

57

Analysis of Robustness for Convex Optimization Applied to Array Antenna Pattern Synthesis  

Microsoft Academic Search

This study presents an analysis of the convex optimization applied to the synthesis of the radiation pattern for linear antenna arrays. This study emphasizes the application of the convex optimization for the array pattern synthesis considering the simultaneous elimination of several zones interferences, reduction of the level of power in two space zones densely populated by interferences, as well as

Richard Torrealba; David H. Covarrubias; Marco Panduro

2008-01-01

58

Solving Semi-Infinite Optimization Problems with Interior Point Techniques  

Microsoft Academic Search

We introduce a new numerical solution method for semi-infinite optimization prob- lems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem func- tions. This approach leads to central path conditions for the lower level problems, where for a given path parameter

Oliver Stein; Georg Still

2003-01-01

59

Applications of Fitzpatrick functions for solving optimization problems  

NASA Astrophysics Data System (ADS)

This paper presents applications of Fitzparick functions to optimization problems. The main purpose of the present work is to introduce applications of the Fitzpatrick functions, involving their specific properties as the maximal monotonicity, or the proper, convex and lower semi-continuity, for solving optimization problems.

Nashed, Z.; Raykov, I.

2012-10-01

60

An Optimal Algorithm for Intersecting Three-Dimensional Convex Polyhedra  

Microsoft Academic Search

This paper describes a linear-time algorithm for computing the intersection of two convex polyhedra in 3-space. Applications of this result to computing intersections, convex hulls, and Voronoi diagrams are also given.

Bernard Chazelle

1992-01-01

61

Planning Locally Optimal, Curvature-Constrained Trajectories in 3D using Sequential Convex Optimization  

E-print Network

, bevel-tip medical needles, planning curvature-constrained channels in 3D printed implants for targeted vehicles (UAVs). In this work, we present a motion planning technique using sequential convex optimization applications. Our experiments indicate that our approach can compute high-quality plans for medical needle

Abbeel, Pieter

62

DEMOS for OPTIMIZATION Problems  

NSDL National Science Digital Library

This demo provides a gallery of visual aids that illustrate fundamental concepts for understanding and developing equations that model optimization problems, commonly referred to as max-min problems. Animations, MATLAB routines and Java applets are included.

Roberts, Lila F.

2002-09-16

63

Convex optimization approach to the fusion of identity information  

NASA Astrophysics Data System (ADS)

We consider the problem of identity fusion for a multi- sensor target tracking system whereby sensors generate reports on the target identities. Since the sensor reports are typically fuzzy, 'incomplete' and inconsistent, the fusion approach based on the minimization of inconsistencies between the sensor reports by using a convex Quadratic Programming (QP) and linear programming (LP) formulation. In contrast to the Dempster-Shafer's evidential reasoning approach which suffers from exponentially growing completely, our approach is highly efficient. Moreover, our approach is capable of fusing 'ratio type' sensor reports, thus it is more general than the evidential reasoning theory. When the sensor reports are consistent, the solution generated by the new fusion method can be shown to converge to the true probability distribution. Simulation work shows that our method generates reasonable fusion results, and when only 'Subset type' sensor reports are presented, it produces fusion results similar to that obtained via the evidential reasoning theory.

Li, Lingjie; Luo, Zhi-Quan; Wong, Kon M.; Bosse, Eloi

1999-03-01

64

Efficient Market Making via Convex Optimization, and a Connection to Online Learning  

E-print Network

X Efficient Market Making via Convex Optimization, and a Connection to Online Learning Jacob illustrate the mathematical paral- lels between cost function based markets and online learning and establish design, securities market, prediction market, automated market maker, convex analysis, online linear

Abernethy, Jake

65

BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS  

E-print Network

BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS Yenming M pattern design, sensor location selection, very large scale arrays, convex op- timization, simulated annealing 1. INTRODUCTION Consider a large scale sensor array having N sensors that monitors a surveillance

Balan, Radu V.

66

Ultrafast Quantum Process Tomography via Continuous Measurement and Convex Optimization  

NASA Astrophysics Data System (ADS)

Quantum process tomography (QPT) is an essential tool to diagnose the implementation of a dynamical map. However, the standard protocol is extremely resource intensive. For a Hilbert space of dimension d, it requires d^2 different input preparations followed by state tomography via the estimation of the expectation values of d^2-1 orthogonal observables. We show that when the process is nearly unitary, we can dramatically improve the efficiency and robustness of QPT through a collective continuous measurement protocol on an ensemble of identically prepared systems. Given the measurement history we obtain the process matrix via a convex program that optimizes a desired cost function. We study two estimators: least-squares and compressive sensing. Both allow rapid QPT due to the condition of complete positivity of the map; this is a powerful constraint to force the process to be physical and consistent with the data. We apply the method to a real experimental implementation, where optimal control is used to perform a unitary map on a d=8 dimensional system of hyperfine levels in cesium atoms, and obtain the measurement record via Faraday spectroscopy of a laser probe.

Baldwin, Charles; Riofrio, Carlos; Deutsch, Ivan

2013-03-01

67

Steepest descent methods for critical points in vector optimization problems  

Microsoft Academic Search

In this article, we present steepest descent methods for finding stationary (critical) points of vector optimization problems for maps from an Euclidean space to a Banach space with respect to the partial order induced by a closed, convex and pointed cone with a nonempty interior. Convergence of the generated sequence to a weakly efficient solution of our problem is established

Thai Doan Chuong; Jen-Chih Yao

2012-01-01

68

Implementation of a Point Algorithm for Real-Time Convex Optimization  

NASA Technical Reports Server (NTRS)

The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.

Acikmese, Behcet; Motaghedi, Shui; Carson, John

2007-01-01

69

Three Extremal Problems for Hyperbolically Convex Functions Roger W. Barnard, Kent Pearce, and G. Brock Williams  

E-print Network

Three Extremal Problems for Hyperbolically Convex Functions Roger W. Barnard, Kent Pearce, and G­9447/$ 2.50 c # 20XX Heldermann Verlag 1 #12; 2 R.W. Barnard, K. Pearce, B. Williams CMFT proper sides

Pearce, Kent

70

libCreme: An optimization library for evaluating convex-roof entanglement measures  

E-print Network

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focussing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems.

Beat Röthlisberger; Jörg Lehmann; Daniel Loss

2011-07-22

71

Level Bundle Methods for Constrained Convex Optimization with ...  

E-print Network

May 23, 2013 ... nonsmooth optimization problems whose objective and constraint functions ... The last few years have seen the occurrence of a new generation of ... We compare the proposed approaches with some algorithms ...... See [1] for such a Unit-Commitment decomposition ..... to hydro-thermal unit-commitment.

2013-05-23

72

Global optimization problems  

Microsoft Academic Search

This chapter introduces readers to the world of continuous global optimization problems.We start with detailed definitions\\u000a of the search space, admissible domain and objective function. The most conventional problem, which consists of finding all\\u000a admissible points in which the objective function has its global extreme, is the basis of further considerations. The next\\u000a problems concern finding local extremes. We also

Robert Schaefer

73

On Projection Algorithms for Solving Convex Feasibility Problems  

Microsoft Academic Search

Due to their extraordinary utility and broad applicability in many areasof classical mathematics and modern physical sciences (most notably,computerized tomography), algorithms for solving convex feasibilityproblems continue to receive great attention. To unify, generalize, andreview some of these algorithms, a very broad and flexible frameworkis investigated . Several crucial new concepts which allow a systematicdiscussion of questions on behaviour in general

Heinz H. Bauschke; Jonathan M. Borwein

1996-01-01

74

Robust fixed-order Hinfinity controller design for spectral models by convex optimization  

Microsoft Academic Search

A new approach for robust fixed-order H1 con- troller design by convex optimization is proposed. Linear time- invariant single-input single-output systems represented by a finite set of complex values in the frequency domain are consi d- ered. It is shown that the H1 robust performance condition can be approximated by a set of linear or convex constraints with respect to

Alireza Karimi; Gorka Galdos; Roland Longchamp

2008-01-01

75

Non-euclidean restricted memory level method for large-scale convex optimization  

Microsoft Academic Search

.  We propose a new subgradient-type method for minimizing extremely large-scale nonsmooth convex functions over simple domains. The characteristic features of the method are (a) the possibility to adjust the scheme to the geometry of the feasible set, thus allowing to get (nearly) dimension-independent (and nearly optimal in the large-scale case) rate-of-convergence results for minimization of a convex Lipschitz continuous function

Aharon Ben-tal; Arkadi Nemirovski

2005-01-01

76

Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach.  

PubMed

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation-elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics. PMID:25232050

Poker, Gilad; Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2014-11-01

77

Subgradient methods for convex minimization  

E-print Network

Many optimization problems arising in various applications require minimization of an objective cost function that is convex but not differentiable. Such a minimization arises, for example, in model construction, system ...

Nedić , Angelia

2002-01-01

78

A multiplicative version of Promethee II applied to multiobjective optimization problems  

Microsoft Academic Search

Abstract The method,Promethee II has produced,attractive results in the choice of the most satisfactory optimal solution of convex multiobjective problems. However, according to the current literature, it may not work properly with nonconvex problems. A modified version of this method, called multiplicative Promethee, is proposed in this paper. Both versions are applied to some analytical problems, previously optimized by an

R. O. Parreiras; João A. Vasconcelos

2007-01-01

79

An algorithm for solving control constrained optimal control problems  

Microsoft Academic Search

An algorithm, with an approach similar to the Han-Powell method in finite-dimensional optimization, is devised to solve continuous-time optimal control problems where the control variables are constrained. The algorithm is based on a second-order approximation to the change of the cost functional due to a change in the control. Further approximation of that summation produces a simple convex functional. It

Baoming Ma; W. S. Levine

1993-01-01

80

libCreme: An optimization library for evaluating convex-roof entanglement measures  

NASA Astrophysics Data System (ADS)

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the MATLAB programming language, but is fully compatible to the free and open-source OCTAVE platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focusing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems. Program summaryProgram title:libCreme Catalogue identifier: AEKD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 3 No. of lines in distributed program, including test data, etc.: 4323 No. of bytes in distributed program, including test data, etc.: 70 542 Distribution format: tar.gz Programming language: Matlab/Octave and C/C++ Computer: All systems running Matlab or Octave Operating system: All systems running Matlab or Octave Classification: 4.9, 4.15 Nature of problem: Evaluate convex-roof entanglement measures. This involves solving a non-linear (unitary) optimization problem. Solution method: Two algorithms are provided: A conjugate-gradient method using a differential-geometric approach and a quasi-Newton method together with a mapping to Euclidean space. Running time: Typically seconds to minutes for a density matrix of a few low-dimensional systems and a decent implementation of the pure-state entanglement measure.

Röthlisberger, Beat; Lehmann, Jörg; Loss, Daniel

2012-01-01

81

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

NASA Astrophysics Data System (ADS)

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

Adhikari, Sam

2007-11-01

82

Adapted Convex Optimization Algorithm for Wavelet-Based Dynamic PET Reconstruction  

E-print Network

1 Adapted Convex Optimization Algorithm for Wavelet-Based Dynamic PET Reconstruction Nelly Abstract--This work deals with Dynamic Positron Emission Tomography (PET) data reconstruction, considering. The effectiveness of this approach is shown with simulated dynamic PET data. Comparative results are also provided

Paris-Sud XI, Université de

83

A Study of Near-Field Direct Antenna Modulation Systems Using Convex Optimization  

E-print Network

) systems. The modulation is carried out in a NFDAM system by means of a control unit that switches amongA Study of Near-Field Direct Antenna Modulation Systems Using Convex Optimization Javad Lavaei de- sign for a class of communication systems known as near-field direct antenna modulation (NFDAM

Hajimiri, Ali

84

10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method  

E-print Network

's method, the formal Newton method began to evolve from Isaac Newton (1669) for finding roots10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method Lecturer: Barnabas Poczos.1 Motivation Newton method is originally developed for finding a root of a function. It is also known as Newton

Tibshirani, Ryan

85

Automated bone segmentation from dental CBCT images using patch-based sparse representation and convex optimization  

SciTech Connect

Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT segmentation based on 15 patients.

Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States)] [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States); Chen, Ken Chung [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China)] [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China); Shen, Steve G. F.; Yan, Jin [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China)] [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Lee, Philip K. M.; Chow, Ben [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China)] [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China); Liu, Nancy X. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China)] [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China); Xia, James J. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States) [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States); Department of Surgery (Oral and Maxillofacial Surgery), Weill Medical College, Cornell University, New York, New York 10065 (United States); Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Shen, Dinggang, E-mail: dgshen@med.unc.edu [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)] [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)

2014-04-15

86

A epsilon-Relaxation Method for Generalized Separable Convex Cost Network Flow Problems  

Microsoft Academic Search

We propose an extension of the -relaxation method to generalized network flow problems with separable convex cost. The method maintains -complementary slackness satisfied at all iterations and adjusts the arc flows and the node prices so to satisfy flow conservation upon termination. Each iteration of the method involves either a price change at a node or a flow change at

Paul Tseng; Dimitri P. Bertsekas

1996-01-01

87

Class and Home Problems: Optimization Problems  

ERIC Educational Resources Information Center

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

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

2011-01-01

88

An ?-relaxation method for separable convex cost generalized network flow problems  

Microsoft Academic Search

.   We generalize the ?-relaxation method of [14] for the single commodity, linear or separable convex cost network flow problem\\u000a to network flow problems with positive gains. The method maintains ?-complementary slackness at all iterations and adjusts\\u000a the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves\\u000a either a

Paul Tseng; Dimitri P. Bertsekas

2000-01-01

89

Tensor completion and low-n-rank tensor recovery via convex optimization  

NASA Astrophysics Data System (ADS)

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas-Rachford splitting technique and its dual variant, the alternating direction method of multipliers.

Gandy, Silvia; Recht, Benjamin; Yamada, Isao

2011-02-01

90

Optimization Problems in Space Geodesy  

NASA Astrophysics Data System (ADS)

In all the computations carried out in Space Geodesy, geodesists are confronted with optimization problems. These latter can roughly be classified in three categories : - Combinatorial problems such as subset problems (search of an instrument sub-network optimizing a given criterion or of an optimal co-location site sub-network), classification problems (division of a global dense GNSS antenna network into several well distributed sub-networks to optimize the computation time), or even minimum cardinal subset problems (optimal selection of basis functions such as wavelets, to represent the Earth's gravity field). - General problems without constraint such as the search for the optimal position, on the Earth's surface, of a new observation instrument. - General problems with constraints such as the determination of optimal weights of heterogeneous data sets in a data processing, or even the computation of satellites orbits. The large amount of data that requires to be processed, together with the possible ill-posed nature of some problems, do not allow us applying classical and/or deterministic approaches. We thus aim to solve all these problems on the basis of stochastic algorithms (possibly hybridized with deterministic methods), such as genetic algorithms. This paper first aims at briefly describing some of the problems summarily listed above, regarding each of the three categories. Then, we summarize the principle and advantages of the genetic algorithms that have been chosen to solve some of the problems. Finally, the design of the algorithm applied and the results obtained are explained for some particular combinatorial problems.

Coulot, D.; Deleflie, F.; Collilieux, X.; Panet, I.; Bernard, E.; Pollet, A.

2010-12-01

91

6.253 Convex Analysis and Optimization, Spring 2004  

E-print Network

6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory ...

Bertsekas, Dimitri

92

Constructing Approximations to the Efficient Set of Convex Quadratic Multiobjective Problems  

E-print Network

programming problem. The method is based on a warm-start interior point algorithm for which we derive classical single-criteria optimization, because different optimal * *points of a multicriteria problem of solutions to a multicriteria optimization problem in* *volves solving a family of single-criteria problems

Fliege, Jörg

93

Interior point decoding for linear vector channels based on convex optimization  

Microsoft Academic Search

In the present paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, which is referred to hereinafter as interior point decoding, is designed for linear vector channels. The linear vector channels include several practically important channels, such as inter-symbol interference channels and partial response (PR) channels. It is shown that

Tadashi Wadayama

2010-01-01

94

Solving convex (and linear) complementarity problems by projection methods (undamped Newton)  

SciTech Connect

A recent approach for solving the Linear Complementarity Problem (LCP) has been the solution of an equivalent system of piecewise linear equations through damped Newton methods. Since these functions are not everywhere differentiable, Newton methods have been adapted to deal with B-differentiable functions. The main drawback of this approach is the need to globalize the results by means of a step-size procedure. We adapt a new method of projections on certain convex sets to solve the LCP. This approach becomes a Newton method with no need of stepsize. Both the theoretical and practical implications are encouraging. The convergence conditions extend with no modifications to a more general convex complementarity problem. If the procedure converges to a nondegenerate solution, the usual Newton quadratic rate of convergence is achieved.

Garcia-Palomares, U.M.

1994-12-31

95

On a non-local perimeter-preserving curve evolution problem for convex plane curves  

Microsoft Academic Search

This paper deals with a non-local evolution problem for closed convex plane curves which preserves the perimeter of the evolving\\u000a curve but enlarges the area it bounds and makes the evolving curve more and more circular during the evolution process. And\\u000a the final shape of the evolving curve will be a circle in the C\\u000a ? metric as the time

Shengliang Pan; Juanna Yang

2008-01-01

96

Applications of convex optimization in signal processing and digital communication  

Microsoft Academic Search

In the last two decades, the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization. These advances have recently started to signifi- cantly impact various fields of applied sciences and engineering where computational efficiency is essential. This paper focuses on two such fields: digital signal processing and communication. In the past, the widely used

Zhi-Quan Luo

2003-01-01

97

Convex optimization methods for graphs and statistical modeling  

E-print Network

An outstanding challenge in many problems throughout science and engineering is to succinctly characterize the relationships among a large number of interacting entities. Models based on graphs form one major thrust in ...

Chandrasekaran, Venkat

2011-01-01

98

A splitting method for separate convex programming - Optimization ...  

E-print Network

Jun 25, 2010 ... The research for the case with general m, however, is in completely ...... reconstruction problems play an important role in various areas of applied sciences such as medical .... This is one of our research topics in the future. 19 ...

2010-06-25

99

Nonnegative Mixed-Norm Convex Optimization for Mitotic Cell Detection in Phase Contrast Microscopy  

PubMed Central

This paper proposes a nonnegative mix-norm convex optimization method for mitotic cell detection. First, we apply an imaging model-based microscopy image segmentation method that exploits phase contrast optics to extract mitotic candidates in the input images. Then, a convex objective function regularized by mix-norm with nonnegative constraint is proposed to induce sparsity and consistence for discriminative representation of deformable objects in a sparse representation scheme. At last, a Support Vector Machine classifier is utilized for mitotic cell modeling and detection. This method can overcome the difficulty in feature formulation for deformable objects and is independent of tracking or temporal inference model. The comparison experiments demonstrate that the proposed method can produce competing results with the state-of-the-art methods. PMID:24348733

Hao, Tong; Gao, Zan; Su, Yuting; Yang, Zhaoxuan

2013-01-01

100

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

PubMed

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders. PMID:25462697

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

2015-01-15

101

BILEVEL OPTIMIZATION PROBLEMS WITH VECTORVALUED ...  

E-print Network

determined for at least one value of the parameter x, problem (1.2) is in general not ... Bilevel programming; multiobjective optimization; linear optimiza- ... over a Pareto set using sequentially improved relaxations of the efficient set is pro-.

2012-05-21

102

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

PubMed

We propose a general framework for determining optimal relationships for tensile strength of doubly convex tablets under diametrical compression. This approach is based on the observation that tensile strength is directly proportional to the breaking force and inversely proportional to a non-linear function of geometric parameters and materials properties. This generalization reduces to the analytical expression commonly used for flat faced tablets, i.e., Hertz solution, and to the empirical relationship currently used in the pharmaceutical industry for convex-faced tablets, i.e., Pitt's equation. Under proper parametrization, optimal tensile strength relationship can be determined from experimental results by minimizing a figure of merit of choice. This optimization is performed under the first-order approximation that a flat faced tablet and a doubly curved tablet have the same tensile strength if they have the same relative density and are made of the same powder, under equivalent manufacturing conditions. Furthermore, we provide a set of recommendations and best practices for assessing the performance of optimal tensile strength relationships in general. Based on these guidelines, we identify two new models, namely the general and mechanistic models, which are effective and predictive alternatives to the tensile strength relationship currently used in the pharmaceutical industry. PMID:25683146

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

2015-04-30

103

OPTIMIZATION OPTIMIZATION  

E-print Network

CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY DATTORRO M #12;Dattorro CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY Meboo #12;Convex Optimization & Euclidean Distance Geometry Jon Dattorro Moo & Euclidean Distance Geometry, Moo, 2005, v2014.04.08. ISBN 0976401304 (English) ISBN 9780615193687

Stanford University

104

THE EXACT FEASIBILITY OF RANDOMIZED SOLUTIONS OF UNCERTAIN CONVEX PROGRAMS  

E-print Network

-supported problems. Key words. Uncertain Optimization, Randomized Methods, Convex Optimization, Semi- Infinite "Identification and adaptive control of indus- trial systems". Universit`a di Brescia - Dipartimento diTHE EXACT FEASIBILITY OF RANDOMIZED SOLUTIONS OF UNCERTAIN CONVEX PROGRAMS M.C. CAMPI AND S

Garatti, Simone

105

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems  

NASA Technical Reports Server (NTRS)

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

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

2012-01-01

106

About an Optimal Visiting Problem  

SciTech Connect

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

Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)

2012-02-15

107

Mapping the Energy Landscape of Non-Convex Optimization Problems  

E-print Network

structure, in which each leaf node rep- resents a local minimum and each non-leaf node represents of Gaussian and learning mixtures of Bernoulli templates. An ELM is a tree structure in which each leaf node represents a local minimum whose energy determines the y-axis position of the leaf node; each non-leaf node

Zhu, Song Chun

108

Optimization and geophysical inverse problems  

SciTech Connect

A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section.

Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.

2000-10-01

109

Interval-Valued Optimization Problems Involving (?, ?)-Right Upper-Dini-Derivative Functions  

PubMed Central

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals. PMID:24982989

2014-01-01

110

A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces  

NASA Astrophysics Data System (ADS)

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem.

Jin, Qinian; Lu, Xiliang

2014-04-01

111

Quadratic Optimization Problems Arising in Computer Vision  

E-print Network

Quadratic Optimization Problems Arising in Computer Vision Jean Gallier Special Thanks to Jianbo a fundamental problem. Unfortunately, I proved Jean Gallier (Upenn) Quadratic Optimization Problems March 23. Jean Gallier (Upenn) Quadratic Optimization Problems March 23, 2011 2 / 61 #12;Perverse Cohomology

Gallier, Jean

112

Quadratic Optimization Problems Arising in Computer Vision  

E-print Network

Quadratic Optimization Problems Arising in Computer Vision Jean Gallier Special Thanks to Jianbo a fundamental problem. Unfortunately, I proved Jean Gallier (Upenn) Quadratic Optimization Problems March 23. Jean Gallier (Upenn) Quadratic Optimization Problems March 23, 2011 2 / 78 #12;Perverse Cohomology

Gallier, Jean

113

Minimum near-convex shape decomposition.  

PubMed

Shape decomposition is a fundamental problem for part-based shape representation. We propose the minimum near-convex decomposition (MNCD) to decompose arbitrary shapes into minimum number of "near-convex" parts. The near-convex shape decomposition is formulated as a discrete optimization problem by minimizing the number of nonintersecting cuts. Two perception rules are imposed as constraints into our objective function to improve the visual naturalness of the decomposition. With the degree of near-convexity a user-specified parameter, our decomposition is robust to local distortions and shape deformation. The optimization can be efficiently solved via binary integer linear programming. Both theoretical analysis and experiment results show that our approach outperforms the state-of-the-art results without introducing redundant parts and thus leads to robust shape representation. PMID:23969396

Ren, Zhou; Yuan, Junsong; Liu, Wenyu

2013-10-01

114

A Bicriterial Optimization Problem of Antenna Design  

Microsoft Academic Search

In this paper we consider a special optimization problem withtwo objectives which arises in antenna theory. It is shown that thisabstract bicriterial optimization problem has at least one solution.Discretized versions of this problem are also discussed, and therelationships between these finite dimensional problems and the infinitedimensional problem are investigated. Moreover, we presentnumerical results for special parameters using a multiobjectiveoptimization method.

Arno Jüschke; Johannes Jahn; Andreas Kirsch

1997-01-01

115

THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAIN  

Microsoft Academic Search

A system of caustics is found for a plane convex domain with a sufficiently smooth boundary; the caustics are close to the boundary and occupy a set of positive measure. A caustic is a convex smooth curve lying in the domain and possessing the property that a tangent to it becomes another tangent to the same curve after reflection from

V F Lazutkin

1973-01-01

116

Reducing of optimal design problems to minimal variational problems  

E-print Network

Reducing of optimal design problems to minimal variational problems Andrej Cherkaev Department of Mathematics The University of Utah Salt Lake City UT 84112 U.S.A. March 28, 1995 Abstract The problems of optimal design of conducting and elastic inhomogeneous bodies is considered; these problems are described

Cherkaev, Andrej

117

Optimal beamforming via interior point methods  

Microsoft Academic Search

We show that two antenna array pattern synthesis problems can be expressed as convex optimization problems. The first one deals with a symmetric planar array with real weights, which can be expressed as a linear program. The second one concerns a broadband acoustic array, which becomes a convex quadratically constrained quadratic program. Because these two problems are convex, they can

Hervé Lebret

1996-01-01

118

An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems  

Microsoft Academic Search

We propose a new fast algorithm for solving one of the standard approaches to\\u000aill-posed linear inverse problems (IPLIP), where a (possibly non-smooth)\\u000aregularizer is minimized under the constraint that the solution explains the\\u000aobservations sufficiently well. Although the regularizer and constraint are\\u000ausually convex, several particular features of these problems (huge\\u000adimensionality, non-smoothness) preclude the use of off-the-shelf optimization

Manya V. Afonso; José M. Bioucas-Dias; Mário A. T. Figueiredo

2011-01-01

119

Automatic Treatment Planning with Convex Imputing  

NASA Astrophysics Data System (ADS)

Current inverse optimization-based treatment planning for radiotherapy requires a set of complex DVH objectives to be simultaneously minimized. This process, known as multi-objective optimization, is challenging due to non-convexity in individual objectives and insufficient knowledge in the tradeoffs among the objective set. As such, clinical practice involves numerous iterations of human intervention that is costly and often inconsistent. In this work, we propose to address treatment planning with convex imputing, a new-data mining technique that explores the existence of a latent convex objective whose optimizer reflects the DVH and dose-shaping properties of previously optimized cases. Using ten clinical prostate cases as the basis for comparison, we imputed a simple least-squares problem from the optimized solutions of the prostate cases, and show that the imputed plans are more consistent than their clinical counterparts in achieving planning goals.

Sayre, G. A.; Ruan, D.

2014-03-01

120

An Optimal Method for Stochastic Composite Optimization  

Microsoft Academic Search

This paper considers an important class of convex programming problems, namely, the stochastic composite optimization (SCO), whose objective function is given by the summation of general nonsmooth and smooth stochastic components. Since SCO covers non-smooth, smooth and stochastic convex optimization as certain special cases, a valid lower bound on the rate of convergence for solving these problems is known from

Guanghui Lan

2009-01-01

121

Applying optimization software libraries to engineering problems  

NASA Technical Reports Server (NTRS)

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.

1984-01-01

122

NP-hardness of deciding convexity of quartic polynomials and related problems  

E-print Network

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves ...

Ahmadi, Amir Ali

123

convex segmentation and mixed-integer footstep planning for a walking robot  

E-print Network

This work presents a novel formulation of the footstep planning problem as a mixed-integer convex optimization. The footstep planning problem involves choosing a set of footstep locations which a walking robot can follow ...

Deits, Robin L. H. (Robin Lloyd Henderson)

2014-01-01

124

Abstract. We consider the problem of finding a point in the intersection of an affine set with a compact convex set, called a convex linear system (CLS). The  

E-print Network

, more efficient algorithms (e.g. interior point methods) require heavy computational cost at eachAbstract. We consider the problem of finding a point in the intersection of an affine set for solving very large scale optimization problems, see e.g., the recent work of Ben-Tal et al. [1]. Indeed

Beck, Amir

125

Optimal impulse control problems and linear programming  

Microsoft Academic Search

Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation

Dario Bauso

2009-01-01

126

The optimal harvesting problem with price uncertainty  

E-print Network

Jul 1, 2011 ... We use stochastic dynamic programming techniques to char- acterize the optimal ... programming was applied to the resolution of the optimal harvesting problem. ...... Solving multistage asset investment prob- lems by the ...

2011-07-01

127

: A New Support Vector Method for Optimizing Partial AUC Based on a Tight Convex Upper Bound  

E-print Network

previous method, the result- ing optimization problem can be solved using a cutting-plane algorithm, Cutting-Plane Method, ROC Curve Permission to make digital or hard copies of all or part of this work plays an important role as an evaluation tool in machine learning and data mining. In particular

Agarwal, Shivani

128

On implementing a primal-dual interior-point method for conic quadratic optimization  

Microsoft Academic Search

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an ane set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can in

Erling D. Andersen; Cornelis Roos; Tamás Terlaky

2003-01-01

129

First and Second Order Necessary Conditions for Stochastic Optimal Control Problems  

SciTech Connect

In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.

Bonnans, J. Frederic, E-mail: Frederic.Bonnans@inria.fr [Ecole Polytechnique, INRIA-Saclay and CMAP (France); Silva, Francisco J., E-mail: fsilva@mat.uniroma1.it [Dipartimento di Matematica Guido Castelnuovo (Italy)

2012-06-15

130

Constrained Graph Optimization: Interdiction and Preservation Problems  

SciTech Connect

The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.

Schild, Aaron V [Los Alamos National Laboratory

2012-07-30

131

An optimal control problem arising in flexible manufacturing systems  

Microsoft Academic Search

A controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems. The existence of a homogeneous Markov nonrandomized optimal policy is established by a convex analytic method. Using the existence of such a policy, the existence of a unique solution in a certain class to the associated Hamilton-Jacobi-Bellman equations is established, and the optimal policy

MRINAL K. GHOSH; ARISTOTLE ARAPOSTATHIS; STEVEN I. MARCUS

1991-01-01

132

Solving optimal control problems with generating functions  

Microsoft Academic Search

The optimal control of a spacecraft as it transitions between specified states in a fixed amount of time is studied. We approach the solution to our optimal control problem with a novel technique, treating the resulting system for the state and adjoints as a Hamiltonian system. We show that the optimal control for this system can be found once the

Daniel J. Scheeres; Vincent Guibout

133

Interior point method for solving optimization problems  

Microsoft Academic Search

In this paper we present a nonlinear optimization method for solving engineering optimal design problems. In addition to maintaining main advantages of typical recursive quadratic methods, our algorithm uses an interior point quadratic programming (QP) subroutine as its QP solver. An implementation of the algorithm proposed in the paper has been applied to standard test problems and real engineering design

Xiong Zhang; Ji Zhou

1995-01-01

134

A Mathematical Optimization Problem in Bioinformatics  

ERIC Educational Resources Information Center

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

Heyer, Laurie J.

2008-01-01

135

Solving combinatorial optimization problems using Karmarkar's algorithm  

Microsoft Academic Search

We describe a cutting plane algorithm for solving combinatorial optimization problems. The primal projective standard-form variant of Karmarkar's algorithm for linear programming is applied to the duals of a sequence of linear programming relaxations of the combinatorial optimization problem.

John E. Mitchell; Michael J. Todd

1992-01-01

136

Fixed, low-order controller design with time response specifications using non-convex optimization.  

PubMed

In this paper, we present a new algorithm for designing a fixed, low-order controller with time response specifications for a linear time invariant (LTI), single input single output (SISO) plant. For a two-parameter feedback configuration, the problem of finding a fixed or low-order controller to meet the desired time response specification is reduced to the least square estimation (LSE) in the sense of partial model matching (PMM), which minimizes a quadratic cost function. The closed-loop stability condition imposed on the controller parameters is formulated by the polynomial matrix inequality (PMI) constraint associated with the cost function. When the cascade feedback structure is considered, the zeros of the controller may be a substantial obstacle when designing a controller that has a good time response. This problem can also be formulated using polynomial constraints. Consequently, it is shown that the total problem here can be formulated as an optimization problem with a quadratic objective function and several polynomial constraints in the controller parameter space. We show that the SeDuMi with YALMIP interface [Löfberg J. YALMIP: A toolbox for modeling and optimization in MATLAB, in: Proceedings of the IEEE symposium on computer aided control systems design 2004. p. 284-9. http://control.ee.ethz.ch/~joloef/yalmip.php] can be used for solving this problem. Finally, several illustrative examples are given. PMID:18606409

Jin, Lihua; Kim, Young Chol

2008-10-01

137

Models for optimal harvest with convex function of growth rate of a population  

SciTech Connect

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma 1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alga Chlorella.

Lyashenko, O.I.

1995-12-10

138

Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization  

E-print Network

address composite optimization problems of the form minimize xRd f(x) := g(x) + h(x), (1) where g and h is 1-regularized least squares [3, 4], minimize xRd Ax - b 2 + x 1, 1 inria-00618152,version1-12Sep of a proximal-gradient method requires the calculation of the proximity operator, proxL(y) = arg min xRd L 2 x

139

Problem Solving through an Optimization Problem in Geometry  

ERIC Educational Resources Information Center

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

Poon, Kin Keung; Wong, Hang-Chi

2011-01-01

140

A Path Following Algorithm for the Graph Matching Problem  

Microsoft Academic Search

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices.

Mikhail Zaslavskiy; Francis R. Bach; Jean-philippe Vert

2009-01-01

141

Path following algorithm for the graph matching problem  

Microsoft Academic Search

Abstract We propose a convex-concave programming,approach for the labeled weighted graph matching problem. The convex-concave programming,formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The

Mikhail Zaslavskiy; Francis Bach; Jean-Philippe Vert

2008-01-01

142

CONSTRAINED POLYNOMIAL OPTIMIZATION PROBLEMS WITH ...  

E-print Network

extract eigenvalue optimizers with an algorithm based on two ingredients: • solution to a .... The algorithm is based on 1-step flat extensions of noncommutative Hankel matrices ...... http://control.ee.ethz.ch/~joloef/wiki/pmwiki.

2012-01-02

143

Large Scale Computational Problems in Numerical Optimization  

SciTech Connect

Our work under this support broadly falls into five categories: automatic differentiation, sparsity, constraints, parallel computation, and applications. Automatic Differentiation (AD): We developed strong practical methods for computing sparse Jacobian and Hessian matrices which arise frequently in large scale optimization problems [10,35]. In addition, we developed a novel view of "structure" in applied problems along with AD techniques that allowed for the efficient application of sparse AD techniques to dense, but structured, problems. Our AD work included development of freely available MATLAB AD software. Sparsity: We developed new effective and practical techniques for exploiting sparsity when solving a variety of optimization problems. These problems include: bound constrained problems, robust regression problems, the null space problem, and sparse orthogonal factorization. Our sparsity work included development of freely available and published software [38,39]. Constraints: Effectively handling constraints in large scale optimization remains a challenge. We developed a number of new approaches to constrained problems with emphasis on trust region methodologies. Parallel Computation: Our work included the development of specifically parallel techniques for the linear algebra tasks underpinning optimization algorithms. Our work contributed to the nonlinear least-squares problem, nonlinear equations, triangular systems, orthogonalization, and linear programming. Applications: Our optimization work is broadly applicable across numerous application domains. Nevertheless we have specifically worked in several application areas including molecular conformation, molecular energy minimization, computational finance, and bone remodeling.

coleman, thomas f. [cornell university] [cornell university

2000-07-01

144

On ''optimal controls for state constraint problems  

E-print Network

On ''­optimal controls for state constraint problems Hitoshi Ishii 3 Department of Mathematics constraint problems. Our method is as follows: We first find feedback laws directly from the associated function of state constraint problems. R' esum' e. -- Nous pr'esentons une m'ethode de construction de

Ishii, Hitoshi

145

Polarimetric SAR tomography in the X-band by continuous wave multi-baseline SAR tracks in a convex optimization approach  

NASA Astrophysics Data System (ADS)

SAR Tomography is the extension of the conventional interferometric radar signal processing, extended in the height dimension. In order to improve the vertical resolution with respect to the classical Fourier methods, high resolution approaches, based on the Convex Optimization (CVX), has been implemented. This methods recast in the Compressed Sensing (CS) framework that optimize tomographic smooth profiles via atomic decomposition, in order to obtain sparsity. The optimum solution has been estimated by Interior Point Methods (IPM). The problem for such kind of signal processing is that the tomographic phase information may be suppressed and only the optimized energy information is available. In this paper we propose a method in order to estimate an optimized spectra and phase information projecting each vector components of each tomographic resolution cell spanned in the real and the imaginary component. The tomographic solutions has been performed by processing multi-baseline SAR datasets, in a full polarimetric mode, acquired by a portable small Continuous Wave (CW) radar in the X band.

Biondi, Filippo; Sarri, Antonio; Fiori, Luca; Dell'Omodarme, Kevin

2014-10-01

146

Hybrid intelligent optimization methods for engineering problems  

Microsoft Academic Search

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients

Yasin Volkan Pehlivanoglu

2010-01-01

147

Comonotonic approximations for optimal portfolio selection problems  

Microsoft Academic Search

We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskless and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of 'constant mix' portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time

J.L.M. Dhaene; Steven Vanduffel; Marc Goovaerts; R. Kaas; David Vyncke

2004-01-01

148

Particle swarm optimization for task assignment problem  

Microsoft Academic Search

Task assignment is one of the core steps to effectively exploit the capabilities of distributed or parallel computing systems. The task assignment problem is an NP-complete problem. In this paper, we present a new task assignment algorithm that is based on the principles of particle swarm optimization (PSO). PSO follows a collaborative population-based search, which models over the social behavior

Ayed Salman; Imtiaz Ahmad; Sabah Al-madani

2002-01-01

149

Hierarchical particle swarm optimizer for minimizing the non-convex potential energy of molecular structure.  

PubMed

The stable conformation of a molecule is greatly important to uncover the secret of its properties and functions. Generally, the conformation of a molecule will be the most stable when it is of the minimum potential energy. Accordingly, the determination of the conformation can be solved in the optimization framework. It is, however, not an easy task to achieve the only conformation with the lowest energy among all the potential ones because of the high complexity of the energy landscape and the exponential computation increasing with molecular size. In this paper, we develop a hierarchical and heterogeneous particle swarm optimizer (HHPSO) to deal with the problem in the minimization of the potential energy. The proposed method is evaluated over a scalable simplified molecular potential energy function with up to 200 degrees of freedom and a realistic energy function of pseudo-ethane molecule. The experimental results are compared with other six PSO variants and four genetic algorithms. The results show HHPSO is significantly better than the compared PSOs with p-value less than 0.01277 over molecular potential energy function. PMID:25459763

Cheung, Ngaam J; Shen, Hong-Bin

2014-11-01

150

An Efficient Interior-Point Method for Convex Multicriteria ...  

E-print Network

specified above by solving the single-objective optimization problem min. zT f(x) ... problem is linear or strictly convex quadratic and the set of feasible points is fixed, i. e. ... interior-point algorithm as presented in [22] is rehearsed in short.

2004-02-25

151

Wind load effect in topology optimization problems  

NASA Astrophysics Data System (ADS)

Topology optimization of two dimensional structures subject to dead and wind loading is considered. The wind loading is introduced into the formulation by using standard expressions for the drag force. A design problem formulation is constructed for minimum compliance design subject to a volume constraint and using the popular SIMP material model. The method of moving asymptotes (MMA) is used to solve the optimization problem. The MMA is modified by including line search and changing the formula for the update of asymptotes. In order to obtain black/white design, intermediate density values, which are used as design variables, are controlled by imposing an explicit constraint. Numerical examples demonstrate that the proposed formulation is successful in incorporating the effect of wind loading into the topology optimization problem.

Zakhama, R.; Abdalla, M. M.; Gürdal, Z.; Smaoui, H.

2007-07-01

152

Quadratic optimization in ill-posed problems  

NASA Astrophysics Data System (ADS)

Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.

Ben Belgacem, F.; Kaber, S.-M.

2008-10-01

153

Linear stochastic optimal control and estimation problem  

NASA Technical Reports Server (NTRS)

Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.

Geyser, L. C.; Lehtinen, F. K. B.

1980-01-01

154

Particle Swarms for Dynamic Optimization Problems  

E-print Network

Particle Swarms for Dynamic Optimization Problems Tim Blackwell1 , J¨urgen Branke2 , and Xiaodong Li3 1 Department of Computing Goldsmiths College, London, UK t.blackwell@gold.ac.uk 2 Institute AIFB- ious authors [9, 7, 14, 17, 19, 20, 21, 32, 29, 38]. The overall consequence of #12;194 T. Blackwell, J

Li, Xiaodong

155

Ant Algorithms Solve Difficult Optimization Problems  

E-print Network

Ant Algorithms Solve Difficult Optimization Problems Marco Dorigo IRIDIA Universit´e Libre de Bruxelles 50 Avenue F. Roosevelt B-1050 Brussels, Belgium mdorigo@ulb.ac.be Abstract. The ant algorithms research field builds on the idea that the study of the behavior of ant colonies or other social insects

Libre de Bruxelles, Université

156

The Global Convergence of Self-Scaling BFGS Algorithmwith Nonmonotone Line Search forUnconstrained Nonconvex Optimization Problems  

Microsoft Academic Search

The self-scaling quasi-Newton method solves an unconstrained optimization problem by\\u000a scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible\\u000a large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved\\u000a in the literature that this method has the global and superlinear convergence when the objective function\\u000a is convex (or

Hong Xia Yin; Dong Lei Du

2007-01-01

157

A Convex Guidance Algorithm for Formation Reconfiguration  

NASA Technical Reports Server (NTRS)

In this paper, a reconfiguration guidance algorithm for formation flying spacecraft is presented. The formation reconfiguration guidance problem is first formulated as a continuous-time minimum-fuel or minimum-energy optimal control problem with collision avoidance and control constraints. The optimal control problem is then discretized to obtain a finite dimensional parameter optimization problem. In this formulation, the collision avoidance constraints are imposed via separating planes between each pair of spacecraft. A heuristic is introduced to choose these separating planes that leads to the convexification of the collision avoidance constraints. Additionally, convex constraints are imposed to guarantee that no collisions occur between discrete time samples. The resulting finite dimensional optimization problem is a second order cone program, for which standard algorithms can compute the global optimum with deterministic convergence and a prescribed level of accuracy. Consequently, the formation reconfiguration algorithm can be implemented onboard a spacecraft for real-time operations.

Acikmese, A. Behcet; Schar, Daniel P.; Murray, Emmanuell A.; Hadaeghs, Fred Y.

2006-01-01

158

From Finite Covariance Windows to Modeling Filters: A Convex Optimization Approach  

Microsoft Academic Search

The trigonometric moment problem is a classical moment problem with numerous applica- tions in mathematics, physics, and engineering. The rational covariance extension problem is a constrained version of this problem, with the constraints arising from the physical re- alizability of the corresponding solutions. Although the maximum entropy method gives one well-known solution, in several applications a wider class of solutions

Christopher I. Byrnes; Sergei V. Gusev; Anders Lindquist

2001-01-01

159

Model results of optimized convex shapes for a solar thermal rocket thruster  

SciTech Connect

A computational, 3-D model for evaluating the performance of solar thermal thrusters is under development. The model combines Monte-Carlo and ray-tracing techniques to follow the ray paths of concentrated solar radiation through an axially symmetric heat-exchanger surface for both convex and concave cavity shapes. The enthalpy of a propellant, typically hydrogen gas, increases as it flows over the outer surface of the absorber/exchanger cavity. Surface temperatures are determined by the requirement that the input radiant power to surface elements balance with the reradiated power and heat conducted to the propellant. The model uses tabulated forms of surface emissivity and gas enthalpy. Temperature profiles result by iteratively calculating surface and propellant temperatures until the solutions converge to stable values. The model provides a means to determine the effectiveness of incorporating a secondary concentrator into the heat-exchanger cavity. A secondary concentrator increases the amount of radiant energy entering the cavity. The model will be used to evaluate the data obtained from upcoming experiments. Characteristics of some absorber/exchanger cavity shapes combined with optionally attached conical secondary concentrators for various propellant flow rates are presented. In addition, shapes that recover some of the diffuse radiant energy which would otherwise not enter the secondary concentrator are considered.

Cartier, S.L. [Sparta Inc., Edwards AFB, CA (United States). Phillips Lab.

1995-11-01

160

On the Coupled Continuous Knapsack Problems:  

E-print Network

... algorithms. Keywords knapsack problem · convex optimization · linearly constrained optimization · ... Obviously, (1) is strictly convex and when the set of its constraints is nonempty, (1) ... there exist many efficient time-linear algorithms to solve (2), as a part of our contribution ... Some common methods are interior point ...

2015-02-17

161

Optimization Online - All Areas Submissions - 2006  

E-print Network

The Effects of Adding Objectives to an Optimization Problem on the Solution Set Joerg Fliege. Convex and Nonsmooth ... the Mathematical Programming Society and by the Optimization Technology Center. Mathematical Programming Society.

162

On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints  

Microsoft Academic Search

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they\\u000a often have a computational advantage over alternatives that have been proposed for solving the same problem and that this\\u000a makes them successful in many real-world applications. This is supported by experimental evidence provided in this paper on\\u000a problems of various sizes (up

Yair Censor; Wei Chen; Patrick L. Combettes; Ran Davidi; Gabor T. Herman

2012-01-01

163

User-guided segmentation of preterm neonate ventricular system from 3-D ultrasound images using convex optimization.  

PubMed

A three-dimensional (3-D) ultrasound (US) system has been developed to monitor the intracranial ventricular system of preterm neonates with intraventricular hemorrhage (IVH) and the resultant dilation of the ventricles (ventriculomegaly). To measure ventricular volume from 3-D US images, a semi-automatic convex optimization-based approach is proposed for segmentation of the cerebral ventricular system in preterm neonates with IVH from 3-D US images. The proposed semi-automatic segmentation method makes use of the convex optimization technique supervised by user-initialized information. Experiments using 58 patient 3-D US images reveal that our proposed approach yielded a mean Dice similarity coefficient of 78.2% compared with the surfaces that were manually contoured, suggesting good agreement between these two segmentations. Additional metrics, the mean absolute distance of 0.65 mm and the maximum absolute distance of 3.2 mm, indicated small distance errors for a voxel spacing of 0.22 × 0.22 × 0.22 mm(3). The Pearson correlation coefficient (r = 0.97, p < 0.001) indicated a significant correlation of algorithm-generated ventricular system volume (VSV) with the manually generated VSV. The calculated minimal detectable difference in ventricular volume change indicated that the proposed segmentation approach with 3-D US images is capable of detecting a VSV difference of 6.5 cm(3) with 95% confidence, suggesting that this approach might be used for monitoring IVH patients' ventricular changes using 3-D US imaging. The mean segmentation times of the graphics processing unit (GPU)- and central processing unit-implemented algorithms were 50 ± 2 and 205 ± 5 s for one 3-D US image, respectively, in addition to 120 ± 10 s for initialization, less than the approximately 35 min required by manual segmentation. In addition, repeatability experiments indicated that the intra-observer variability ranges from 6.5% to 7.5%, and the inter-observer variability is 8.5% in terms of the coefficient of variation of the Dice similarity coefficient. The intra-class correlation coefficient for ventricular system volume measurements for each independent observer ranged from 0.988 to 0.996 and was 0.945 for three different observers. The coefficient of variation and intra-class correlation coefficient revealed that the intra- and inter-observer variability of the proposed approach introduced by the user initialization was small, indicating good reproducibility, independent of different users. PMID:25542486

Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; McLeod, Jonathan; Chen, Yimin; de Ribaupierre, Sandrine; Fenster, Aaron

2015-02-01

164

Optimal Investment Problems with Marked Point Processes  

Microsoft Academic Search

\\u000a Optimal investment problems in an incomplete financial market with pure jump stock dynamics are studied. An investor with\\u000a Constant Relative Risk Aversion (CRRA) preferences, including the logarithmic utility, wants to maximize her\\/his expected\\u000a utility of terminal wealth by investing in a bond and in a risky asset. The risky asset price is modeled as a geometric marked\\u000a point process, whose

Claudia Ceci

165

Stability properties of KKT points in vector optimization  

Microsoft Academic Search

In this article we introduce the notion of approximate Karush–Kuhn–Tucker (KKT) points for smooth, convex and nonsmooth, nonconvex vector optimization problems. We study a kind of stability of these points and KKT points of vector optimization problems. In the convex case we also introduce and study the notion of modified approximate KKT points motivated by Ekeland's variational principle. We prove

Marius Durea; J. Dutta; Chr. Tammer

2011-01-01

166

MOMMOP: Multiobjective Optimization for Locating Multiple Optimal Solutions of Multimodal Optimization Problems.  

PubMed

In the field of evolutionary computation, there has been a growing interest in applying evolutionary algorithms to solve multimodal optimization problems (MMOPs). Due to the fact that an MMOP involves multiple optimal solutions, many niching methods have been suggested and incorporated into evolutionary algorithms for locating such optimal solutions in a single run. In this paper, we propose a novel transformation technique based on multiobjective optimization for MMOPs, called MOMMOP. MOMMOP transforms an MMOP into a multiobjective optimization problem with two conflicting objectives. After the above transformation, all the optimal solutions of an MMOP become the Pareto optimal solutions of the transformed problem. Thus, multiobjective evolutionary algorithms can be readily applied to find a set of representative Pareto optimal solutions of the transformed problem, and as a result, multiple optimal solutions of the original MMOP could also be simultaneously located in a single run. In principle, MOMMOP is an implicit niching method. In this paper, we also discuss two issues in MOMMOP and introduce two new comparison criteria. MOMMOP has been used to solve 20 multimodal benchmark test functions, after combining with nondominated sorting and differential evolution. Systematic experiments have indicated that MOMMOP outperforms a number of methods for multimodal optimization, including four recent methods at the 2013 IEEE Congress on Evolutionary Computation, four state-of-the-art single-objective optimization based methods, and two well-known multiobjective optimization based approaches. PMID:25099966

Wang, Yong; Li, Han-Xiong; Yen, Gary G; Song, Wu

2015-04-01

167

On the state-space design of optimal controllers for distributed systems with finite communication speed  

Microsoft Academic Search

We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which such controllers can be described. We show that the optimal control problem is not convex with respect to certain state-space design parameters, and demonstrate a reasonable relaxation that renders the problem convex. This relaxation is associated with

Makan Fardad; Mihailo R. Jovanovic

2008-01-01

168

PLASMA Approximate Dynamic Programming finally cracks the locomotive optimization problem  

E-print Network

PLASMA ­ Approximate Dynamic Programming finally cracks the locomotive optimization problem programming to optimize the flows of locomotives over their networks. The problem was always to be handled if a model is going to accurately capture locomotive productivity. In addition

Powell, Warren B.

169

LDRD Final Report: Global Optimization for Engineering Science Problems  

SciTech Connect

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

HART,WILLIAM E.

1999-12-01

170

PIECEWISE QUADRATIC APPROXIMATIONS IN CONVEX ...  

E-print Network

For instance, the recent [31] uses a different model ...... Fortunately, increasing ? and/or ? is a reaction to the fact that the ? obtained by ..... Piecewise quadratic approximations in convex numerical optimization. 25 name n function. 1 CB2. 2.

2010-12-11

171

Coordination and control of distributed spacecraft systems using convex optimization techniques  

Microsoft Academic Search

SUMMARY Formation flying of multiple spacecraft is an enabling technology for many future space science missions. However, the co-ordination and control of these instruments poses many difficult design challenges. This paper presents fuel\\/time-optimal control algorithms for a co-ordination and control architecture that was designed for a fleet of spacecraft. This architecture includes low-level formation-keeping algorithms and a high-level fleet planner

Michael Tillerson; Gokhan Inalhan; Jonathan P. How

2002-01-01

172

Optimal Planning and Problem-Solving  

NASA Technical Reports Server (NTRS)

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

Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg

2008-01-01

173

RELIABLE SOLUTION OF CONVEX QUADRATIC PROGRAMS ...  

E-print Network

Key words. active set, convex, homotopy method, parametric quadratic programming ... impluse response design, optimal power flow, economic dispatch, etc. Several ... *Interdisciplinary Center for Scientific Computing, Heidelberg University, ...

2011-01-28

174

Solving Customer-Driven Microgrid Optimization Problems as DCOPs  

E-print Network

Solving Customer-Driven Microgrid Optimization Problems as DCOPs Saurabh Gupta , Palak Jain common customer-driven microgrid (CDMG) optimization problems ­ a comprehensive CDMG optimization problem that there is an urgent need to move away from fossil fuel to renewable energy resources given that the demand for fossil

Yeoh, William

175

High Performance Grid and Cluster Computing for Some Optimization Problems  

Microsoft Academic Search

Solving large scale optimization problems requires a huge amount of computational power. The size of optimization problems that can be solved on a few CPUs has been lim- ited due to a lack of computational power. Grid and cluster computing has received much attention as a powerful and inexpensive way of solving large scale optimization problems that an existing single-unit

Katsuki Fujisaway; Masakazu Kojimaz; Akiko Takeda; Makoto Yamashita

176

A computational study of the homogeneous algorithm for largescale convex optimization  

E-print Network

. Andersen \\Lambda Yinyu Ye y May 1996 (Revised marts 1997) Abstract Recently the authors have proposed and DMI­9522507. 1 #12; Key words: Monotone complementarity problem, homogeneous and self­dual model and practical behavior of the primal­dual interior­point methods for solving general or specific classes

Ye, Yinyu

177

Hybrid intelligent optimization methods for engineering problems  

NASA Astrophysics Data System (ADS)

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles.

Pehlivanoglu, Yasin Volkan

178

An efficient method to compute traffic assignment problems with ...  

E-print Network

By convexity, the Lagrangian dual problem has the same optimal value as (4). A quick inspection ... units from an origin node to a destination node. The following .... The standard termination criterion is a small enough relative optimality gap:.

2006-07-26

179

Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results  

Microsoft Academic Search

Given a (combinatorial) optimization problem and a feasible solution to it, the correspond- ing inverse optimization problem is to nd a minimal adjustment of the cost function such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods

Clemens Heuberger

2004-01-01

180

Inverse Optimization: A Survey on Problems, Methods, and Results  

Microsoft Academic Search

Given a (combinatorial) optimization problem and a feasible solution to it, the correspondinginverse optimization problem is to nd a minimal adjustment of the parameters of theproblem (costs, capacities, . . . ) such that the given solution becomes optimum.Several such problems have been studied in the last ten years. After formalizing the notionof an inverse problem and its variants, we

Clemens Heuberger

2003-01-01

181

Interior-point methods for convex programming  

Microsoft Academic Search

This work is concerned with generalized convex programming problems, where the objective function and also the constraints belong to a certain class of convex functions. It examines the relationship of two basic conditions used in interior-point methods for generalized convex programming—self-concordance and a relative Lipschitz condition—and gives a short and simple complexity analysis of an interior-point method for generalized convex

Florian Jarre

1992-01-01

182

A quadratically convergent Newton method for vector optimization  

E-print Network

We propose a Newton method for solving smooth unconstrained vector optimization problems ...... ical Economics, 40 (2004), pp. 683-699. [2] C.D. ... [4] D. Bertsekas, Convex Analysis and Optimization, Athena Scientific,. Belmont, 2003. 20 ...

2011-07-27

183

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

NASA Technical Reports Server (NTRS)

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

Nguyen, Duc T.

1990-01-01

184

Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems  

Microsoft Academic Search

Whether or not the general asymmetric variational inequality problem can be formulated as a differentiable optimization problem has been an open question. This paper gives an affirmative answer to this question. We provide a new optimization problem formulation of the variational inequality problem, and show that its objective function is continuously differentiable whenever the mapping involved in the latter problem

Masao Fukushima

1992-01-01

185

Group search optimizer for the mobile location management problem.  

PubMed

We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199

Wang, Dan; Xiong, Congcong; Huang, Wei

2014-01-01

186

Group Search Optimizer for the Mobile Location Management Problem  

PubMed Central

We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199

Wang, Dan; Xiong, Congcong; Huang, Wei

2014-01-01

187

Fast Approximate Convex Decomposition  

E-print Network

Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can...

Ghosh, Mukulika

2012-10-19

188

Optimal shape design as a material distribution problem  

Microsoft Academic Search

Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a

M. P. Bendsøe

1989-01-01

189

An analytical comparison of optimization problem generation methodologies  

Microsoft Academic Search

Heuristics are an increasingly popular solution method for combinatorial optimization problems. Heuristic use often frees the modeler from some of the restrictions placed on classical optimization methods required to constrain prob- lem complexity. As a result, modelers are using heuristics to tackle problems previously considered unsolvable, im- prove performance over classical optimization methods, and open new avenues of empirical study.

Raymond R. Hill

1998-01-01

190

A Constructive algorithm to solve "convex recursive deletion" (CoRD) classification problems via two-layer perceptron networks  

E-print Network

two-layer perceptron networks by C. Cabrelli1 , U. Molter1 Departamento de Matem´atica, Facultad de-layer Perceptron) using threshold activation functions is that either it be a convex polytope, or that intersected not be arbitrarily large. An artificial Neural Network consisting of a single such neuron is known as a Perceptron

Cabrelli, Carlos

191

Existence of classical solutions to a free boundary problem for the pLaplace operator: (II) the interior convex case  

E-print Network

) the interior convex case Antoine HENROT \\Lambda Equipe de Math'ematiques, UMR CNRS Universit'e de Franche­Comt of Mathematics Royal Institute of Technology 100 44 Stockholm SWEDEN email henriks@math.kth.se August 11, 1999

Shahgholian, Henrik

192

Ant Colony Optimization and the minimum spanning tree problem  

Microsoft Academic Search

Ant Colony Optimization (ACO) is a kind of metaheuristic that has become very popular for solving problems from combinatorial optimization. Solutions for a given problem are constructed by a random walk on a so-called construction graph. This random walk can be influenced by heuristic information about the problem. In contrast to many successful applications, the theoretical foundation of this kind

Frank Neumann; Carsten Witt

2010-01-01

193

A fuzzy satisficing method for multiobjective linear optimal control problems  

Microsoft Academic Search

In this paper, we propose a fuzzy satisficing method for the solution of multiobjective linear continuous optimal control problems. To solve these multiobjective linear continuous optimal control problems, we first discretize the time and replace the system of differential equations by difference equations. By introducing suitable auxiliary variables, approximate linear multiobjective programming problems are formulated. Then by considering the vague

Masatoshi Sakawa; Masahiro Inuiguchi; Kosuke Kato; Tomohiro Ikeda

1996-01-01

194

Numerical methods for solving applied optimal control problems  

NASA Astrophysics Data System (ADS)

For an optimal control problem with state constraints, an iterative solution method is described based on reduction to a finite-dimensional problem, followed by applying a successive linearization algorithm with the use of an augmented Lagrangian. The efficiency of taking into account state constraints in optimal control computation is illustrated by numerically solving several application problems.

Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.

2013-12-01

195

On convex relaxation of graph isomorphism.  

PubMed

We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving [Formula: see text] equality and [Formula: see text] inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic. PMID:25713342

Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron

2015-03-10

196

Methods for optimizing over the efficient and weakly efficient sets of an affine fractional vector optimization program  

Microsoft Academic Search

Both the efficient and weakly efficient sets of an affine fractional vector optimization problem, in general, are neither convex nor given explicitly. Optimization problems over one of these sets are thus nonconvex. We propose two methods for optimizing a real-valued function over the efficient and weakly efficient sets of an affine fractional vector optimization problem. The first method is a

Le Thi Hoai An; Pham Dinh Tao; Nguyen Canh Nam; Le Dung Muu

2010-01-01

197

First-order convex feasibility algorithms for x-ray CT  

SciTech Connect

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 Degree-Sign . 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.

Sidky, Emil Y.; Pan Xiaochuan [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois, 60637 (United States); Jorgensen, Jakob S. [Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet, Building 303B, 2800 Kongens Lyngby (Denmark)

2013-03-15

198

First-order convex feasibility algorithms for x-ray CT  

PubMed Central

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

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

2013-01-01

199

Necessarily efficient solutions of multiobjective linear optimal control problems  

Microsoft Academic Search

We consider multiobjective linear programming problem with interval objective functions. One solution for this problem is called a necessarily efficient solution, that is efficient for every possible perturbation of coefficients within given intervals, which can be regarded as a kind of robust solution for optimal control problems. We improve the simplex based multiobjective problem solving method for generating a set

Ida Masaaki

1997-01-01

200

The Traveling Salesman Problem: A Case Study in Local Optimization  

Microsoft Academic Search

This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, London, 1997, pp. 215-310. The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial optimization, including clas- sical local optimization techniques as well

David S. Johnson; Lyle A. McGeoch

1977-01-01

201

A Distributed Optimization Approach to Constrained OSNR Problem  

E-print Network

A Distributed Optimization Approach to Constrained OSNR Problem Yan Pan Tansu Alpcan Lacra Pavel signal-to-noise ratio (OSNR) problem via a distributed optimization approach. In multi-channel optical to OSNR degradation. Regulating the input optical power at the Source (transmitter) aims to achieve

Pavel, Lacra

202

Differential Evolution Applied to a Multimodal Information Theoretic Optimization Problem  

Microsoft Academic Search

This paper discusses the problems raised by the optimization of a mu- tual information-based objective function, in the context of a multimodal speaker detection. As no approximation is used, this function is highly nonlinear and plagued by numerous local minima. Three different optimization methods are compared. The Differential Evolution algorithm is deemed to be the best for the problem at

Patricia Besson; Jean-marc Vesin; Vlad Popovici; Murat Kunt

2006-01-01

203

A Genetic Algorithm for Minimax Optimization Problems Jeffrey W. Herrmann  

E-print Network

A Genetic Algorithm for Minimax Optimization Problems Jeffrey W. Herrmann Department of Mechanical-space genetic algorithm as a general technique to solve minimax optimization problems. This algorithm maintains of applications. To illustrate its potential, we use the two-space genetic algorithm to solve a parallel machine

Herrmann, Jeffrey W.

204

Stability of Merton's portfolio optimization problem for Lévy models  

Microsoft Academic Search

Merton's classical portfolio optimization problem for an investor, who can trade in a risk-free bond and a stock, can be extended to the case where the driving noise of the logreturns is a pure jump process instead of a Brownian motion. Benth et al. [4,5] solved the problem and found the optimal control implicitly given by an integral equation in

Fred Espen Benth; Maren Diane Schmeck

2012-01-01

205

High Performance Grid and Cluster Computing for Some Optimization Problems  

Microsoft Academic Search

The aim of this short article is to show that grid and cluster computing provides tremendous power to optimization methods. The methods that the article picks up are a successive con- vex relaxation method for quadratic optimization problems, a polyhedral homotopy method for polynomial systems of equations and a primal-dual interior-point method for semidefi- nite programming problems. Their parallel implementations

Katsuki Fujisawa; Masakazu Kojima; Akiko Takeda; Makoto Yamashita

2004-01-01

206

NECESSARY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS  

Microsoft Academic Search

Necessary conditions of optimality are derived for optimal control problems with pathwise state constraints, in which the dynamic constraint is modelled as a dierential inclusion. The novel feature of the conditions is the unrestrictive nature of the hypotheses under which these conditions are shown to be valid. An Euler Lagrange type condition is obtained for problems where the multifunction associated

R. B. VINTER; H. ZHENG

207

Par reduction in OFDM through convex programming  

Microsoft Academic Search

The high peak-to-average power ratio (PAR) encountered in OFDM system has been a major obstacle in the implementation of power efficient transmitter. In this paper, we present a new active constellation extension (ACE) based convex optimization algorithm which reduces PAR through convex programming. In comparison with previous convex programming method, our method greatly reduces the complexity and keeps the bit-error-rate

Chao Wang; Shu Hung Leung

2008-01-01

208

An exact solution to the transistor sizing problem for CMOS circuits using convex optimization  

Microsoft Academic Search

Abstract: this paper.Given the MOS circuit topology, the delay can be controlled byvarying the sizesof transistors in the circuit. Here, the size of a transistor is measured in terms of its channelwidth, since the channel lengths in a digital circuit are generally uniform. Roughly speaking,the sizes of certain transistors can be increased to reduce the circuit delay at the expense

Sachin S. Sapatnekar; Vasant B. Rao; Pravin M. Vaidya; Sung-mo Kang

1993-01-01

209

Ant Colony Optimization and the Minimum Spanning Tree Problem  

Microsoft Academic Search

Ant Colony Optimization (ACO) is a kind of metaheuristic that has become very popular for solving problems from combinatorial\\u000a optimization. Solutions for a given problem are constructed by a random walk on a so-called construction graph. This random\\u000a walk can be influenced by heuristic information about the problem. In contrast to many successful applications, the theoretical\\u000a foundation of this kind

Frank Neumann; Carsten Witt

2007-01-01

210

Exploiting Problem Structure for Distributed Constraint Optimization  

E-print Network

constraint satisfaction to enforce problem constraints and constraints imposed by the anchor agent. We focus our study on the well­known NP­complete job shop scheduling problem. We define and study two problem structure measures, disparity ratio and disparity composition ratio. We experimentally evaluated

Yu, Bin

211

Convergent relaxations of polynomial optimization problems with ...  

E-print Network

2Institute for Mathematical Sciences, Imperial College London .... ear combination p = ? w ..... The definition (15) of ?·, ·? induces a well defined inner product on the quotient ...... Yalmip : A toolbox for modeling and optimization in MATLAB.

2010-01-11

212

Singular perturbation analysis of AOTV-related trajectory optimization problems  

NASA Technical Reports Server (NTRS)

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

Calise, Anthony J.; Bae, Gyoung H.

1990-01-01

213

Theory on the Tracks: A Selection of Railway Optimization Problems  

Microsoft Academic Search

Railway optimization problems have been studied from a mathematical pro- gramming perspective for decades. This approach is particularly well suited to model the multitude of constraints that typically arises in the context of a railway system. In recent years, these problems have attracted some at- tention in the algorithms community, with a focus on individual problem aspects, in an attempt

Michael Gatto; Riko Jacob; Leon Peeters; Birgitta Weber; Peter Widmayer

214

THE MOLECULE PROBLEM EXPLOITING STRUCTURE IN GLOBAL OPTIMIZATION \\Lambda  

E-print Network

THE MOLECULE PROBLEM EXPLOITING STRUCTURE IN GLOBAL OPTIMIZATION \\Lambda BRUCE HENDRICKSON y Abstract. The molecule problem is that of determining the relative locations of a set of objects applications in the determination of molecular conformation. The molecule problem can be naturally expressed

Hendrickson, Bruce

215

Optimized Waveform Relaxation Solution of Electromagnetic and Circuit Problems  

E-print Network

a method for the parallel solution of time domain combined ElectroMagetic (EM) and circuit problems. The EM1 Optimized Waveform Relaxation Solution of Electromagnetic and Circuit Problems Martin J. Gander-- New algorithms are needed to solve electromagnetic problems using today's widely available parallel

Gander, Martin J.

216

GLOBAL OPTIMIZATION FOR THE PHASE AND CHEMICAL EQUILIBRIUM PROBLEM  

E-print Network

GLOBAL OPTIMIZATION FOR THE PHASE AND CHEMICAL EQUILIBRIUM PROBLEM: APPLICATION TO THE NRTL of solutions to the phase and chemical equilibrium problem when the problem is posed as the minimization the equilibrium condition. For many chemical engineering applications this function will be the Gibbs free energy

Neumaier, Arnold

217

Location problems optimization by a self-organizing multiagent approach  

Microsoft Academic Search

The Facility Location Problem (FLP) requires locating facilities in or- der to optimize some performance criteria. This problem occurs in many practical settings where facilities provide a service, such as the location of plants, bus-stops, fire stations, etc. Particularly, we deal with the con- tinuous version of location problem where facilities have to be located in an Euclidean plane. This

Sana Moujahed; Olivier Simonin; Abderrafiaa Koukam

2009-01-01

218

Graph Implementations for Nonsmooth Convex Programs  

E-print Network

programming, conic optimization, nondifferentiable functions. 1 Introduction It is well known that convex, as well as for certain standard forms such as semidefinite programs (SDPs), that are efficient in bothGraph Implementations for Nonsmooth Convex Programs Michael C. Grant I and Stephen P. Boyd 2 1

219

A Planning Problem Combining Calculus of Variations and Optimal Transport  

SciTech Connect

We consider some variants of the classical optimal transport where not only one optimizes over couplings between some variables x and y but also over some control variables governing the evolutions of these variables with time. Such a situation is motivated by an assignment problem of tasks with workers whose characteristics can evolve with time (and be controlled). We distinguish between the coupled and decoupled case. The coupled case is a standard optimal transport with the value of some optimal control problem as cost. The decoupled case is more involved since it is nonlinear in the transport plan.

Carlier, G., E-mail: carlier@ceremade.dauphine.fr; Lachapelle, A., E-mail: lachapelle@ceremade.dauphine.f [Universite Paris IX Dauphine, CEREMADE, UMR CNRS 7534 (France)

2011-02-15

220

Optimal Control of the Obstacle Problem in a Perforated Domain  

SciTech Connect

We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly on the rate at which the size of the holes shrink.

Stroemqvist, Martin H., E-mail: stromqv@kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)

2012-10-15

221

Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution  

Microsoft Academic Search

We concentrate here on decomposition of 2D objects into mean- ingful parts of visual form ,o rvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identify- ing convex parts at

Longin Jan Latecki; Rolf Lakämper

1999-01-01

222

? Conservative approximation for probabilistically constrained convex programs  

Microsoft Academic Search

In this paper, we address an approximate solution of a probabilistically constrained convex program (PCCP), where a convex\\u000a objective function is minimized over solutions satisfying, with a given probability, convex constraints that are parameterized\\u000a by random variables. In order to approach to a solution, we set forth a conservative approximation problem by introducing\\u000a a parameter ? which indicates an approximate

Yuichi Takano; Jun-ya Gotoh

2010-01-01

223

Checking for Optimal Solutions in Some NP-Complete Problems  

NASA Astrophysics Data System (ADS)

For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.

Bauer, Michel; Orland, Henri

2005-09-01

224

Spectral finite-element methods for parametric constrained optimization problems.  

SciTech Connect

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.

Anitescu, M.; Mathematics and Computer Science

2009-01-01

225

Comparison of optimal design methods in inverse problems  

NASA Astrophysics Data System (ADS)

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

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

2011-07-01

226

Optimal measurements for the dihedral hidden subgroup problem  

E-print Network

We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success probability of this measurement exhibits a sharp threshold as a function of the density nu=k/log N, where k is the number of copies of the hidden subgroup state and 2N is the order of the dihedral group. In particular, for nua probability that is exponentially small in log N, while for nu>1 the optimal measurement identifies the hidden subgroup with a probability of order unity. Thus the dihedral group provides an example of a group G for which Omega(log|G|) hidden subgroup states are necessary to solve the hidden subgroup problem. We also consider the optimal measurement for determining a single bit of the answer, and show that it exhibits the same threshold. Finally, we consider implementing the optimal measurement by a quantum circuit, and thereby establish further connections between the dihedral hidden subgroup problem and average case subset sum problems. In particular, we show that an efficient quantum algorithm for a restricted version of the optimal measurement would imply an efficient quantum algorithm for the subset sum problem, and conversely, that the ability to quantum sample from subset sum solutions allows one to implement the optimal measurement.

Dave Bacon; Andrew M. Childs; Wim van Dam

2005-04-26

227

A cavity approach to optimization and inverse dynamical problems  

E-print Network

In these two lectures we shall discuss how the cavity approach can be used efficiently to study optimization problems with global (topological) constraints and how the same techniques can be generalized to study inverse problems in irreversible dynamical processes. These two classes of problems are formally very similar: they both require an efficient procedure to trace over all trajectories of either auxiliary variables which enforce global constraints, or directly dynamical variables defining the inverse dynamical problems. We will mention three basic examples, namely the Minimum Steiner Tree problem, the inverse threshold linear dynamical problem, and the zero patient problem in epidemic cascades. All these examples are root problems in optimization and inference over networks. They appear in many modern applications and in a variety of different contexts. Credit for these results should be shared with A. Braunstein, A. Ramezanpour, F. Altarelli, L. Dall'Asta, and A. Lage-Castellanos.

Lage-Castellanos, Alejandro; Zecchina, Riccardo

2014-01-01

228

Identifying superfluous constraints within an interior-point algorithm for convex quadratic programming  

Microsoft Academic Search

In this article, quadratic programming problems with strict convex objective functions f and linear constraints are considered. Based on a nonlinear separation Theorem, a complete characterization of constraints that are superfluous in an optimal point is given. It allows to derive sufficient conditions for deletion of restrictions. The corresponding conditions can easily be checked if upper bounds on the objective

P. Recht; P. H. Schade

2007-01-01

229

On complexity of stochastic programming problems - Optimization ...  

E-print Network

would like to make such decisions in a reasonably optimal way. Then for ... There are several natural questions which arise with respect to formulation (1.1). ...... t = 0, one has $ 1, and should decide how to distribute this money between stocks.

2005-01-14

230

Optimal Control Formulations of Vibration Reduction Problems  

Microsoft Academic Search

Design of controls to move a flexible body such as a robot arm while minimizing unwanted vibrations has been described in many papers and presented in many forms. For the vibration reduction issue alone, it is shown that almost all the proposed designs can be formulated as optimal controls of either the fixed final time or the minimum time type.

Abhishek Dhanda; Gene F. Franklin

2010-01-01

231

1 Statement of the problem - Optimization Online  

E-print Network

Its endpoint B obviously lies in the first quadrant with y(B) > 0. a b. Figure 3: Connect the center O1 of left circle with the point B by a straight line. Let the arc A B be .... For any point from Q1 ? Q2 the lower extremal of type Ib is optimal. Type IIb.

2012-05-23

232

introduction first problem two optimization problems in physiology  

E-print Network

: homogeneous functional behavior (focused on tracer metabolism) input for kinetics: FDG concentration in blood first problem FDG-PET FDG is a glucose analog that allows tracking glucose metabolism glucose compartmental analysis concept: compartment: homogeneous functional behavior (focused on tracer metabolism

Combettes, Patrick Louis

233

Cut Generation for Optimization Problems with Multivariate Risk ...  

E-print Network

Aug 14, 2014 ... and Rudolf (2013) found the homeland security allocation problem instances featuring up to 500 scenarios ...... this operation does not change the set of optimal solutions. ...... where c? ? R4 is a center satisfying c?.

2014-08-14

234

Parallel evolutionary algorithms for optimization problems in aerospace engineering  

NASA Astrophysics Data System (ADS)

This paper presents the recent developments in hierarchical genetic algorithms (HGAs) to speed up the optimization of aerodynamic shapes. It first introduces HGAs, a particular instance of parallel GAs based on the notion of interconnected sub-populations evolving independently. Previous studies have shown the advantages of introducing a multi-layered hierarchical topology in parallel GAs. Such a topology allows the use of multiple models for optimization problems, and shows that it is possible to mix fast low-fidelity models for exploration and expensive high-fidelity models for exploitation. Finally, a new class of multi-objective optimizers mixing HGAs and Nash Game Theory is defined. These methods are tested for solving design optimization problems in aerodynamics. A parallel version of this approach running a cluster of PCs demonstrate the convergence speed up on an inverse nozzle problem and a high-lift problem for a multiple element airfoil.

Wang, J. F.; Periaux, J.; Sefrioui, M.

2002-12-01

235

Decomposition methods for large scale stochastic and robust optimization problems  

E-print Network

We propose new decomposition methods for use on broad families of stochastic and robust optimization problems in order to yield tractable approaches for large-scale real world application. We introduce a new type of a ...

Becker, Adrian Bernard Druke

2011-01-01

236

Direct Multiple Shooting Optimization with Variable Problem Parameters  

NASA Technical Reports Server (NTRS)

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

Whitley, Ryan J.; Ocampo, Cesar A.

2009-01-01

237

New Hybrid Optimization Algorithms for Machine Scheduling Problems  

E-print Network

decision (or constraint satisfaction) problems resulting from a dichotomy to locate the .... is allowed to start at time rj; once started, the job will occupy the machine ...... the theory and applications of large-scale optimization algorithms, discrete.

2006-12-03

238

Non-concave and behavioural optimal portfolio choice problems   

E-print Network

Our aim is to examine the problem of optimal asset allocation for investors exhibiting a behaviour in the face of uncertainty which is not consistent with the usual axioms of Expected Utility Theory. This thesis is divided ...

Meireles Rodrigues, Andrea Sofia; Rodrigues, Andrea

2014-11-27

239

A polynomial-time interior-point method for conic optimization, with ...  

E-print Network

Interior-point methods (IPMs) are the algorithms of choice for solving many convex opti- ... most efficient algorithms require barrier functions for both the primal and dual problems. ... method for linear optimization problems can in principle be applied to conic .... Let S ? Rn be a closed convex set with nonempty interior.

2008-04-29

240

Improved Approximation Bound for Quadratic Optimization Problems ...  

E-print Network

Nov 21, 2007 ... Beginning with the seminal work of Goemans and Williamson. [8], who showed .... suitable orthogonal transformation to S to obtain vectors v?. 1,...,v? mn ..... Assignment Problems and the Location of Economic. Activities.

2007-11-21

241

Multitask principal-agent problems: Optimal contracts, fragility, and effort misallocation  

Microsoft Academic Search

We analyze a tractable class of multitask principal-agent problems, such as the one faced by a firm with a manager overseeing several projects. We allow for tasks to be complements or substitutes. We avoid the problems associated with the first-order approach by directly characterizing the shape of the agent's indirect utility function, which exhibits a convex then concave shape in

Philip Bond; Armando Gomes

2007-01-01

242

Hybrid Evolutionary Algorithm for Solving Global Optimization Problems  

Microsoft Academic Search

Differential Evolution (DE) is a novel evolutionary approach capable of handling non-differentiable, non-linear and multi-modal objective functions. DE has been consistently ranked as one of the best search algorithm for solving global optimization problems in several case studies. This paper presents a simple and modified hybridized Differential Evolution algorithm for solving global optimization problems. The proposed algorithm is a hybrid

Radha Thangaraj; Millie Pant; Ajith Abraham; Youakim Badr

2009-01-01

243

Runge-Kutta Discretizations of Optimal Control Problems  

E-print Network

Runge-Kutta Discretizations of Optimal Control Problems #3; William W. Hager Department of results for the error associated with Runge-Kutta discretizations. Key words. Optimal control, numerical solution, discretization, Runge-Kutta scheme, rate of convergence. AMS(MOS) subject classi#12;cations. 49M

Hager, William

244

Finding Optimal Gains In Linear-Quadratic Control Problems  

NASA Technical Reports Server (NTRS)

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

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

1990-01-01

245

CORRELATIVE SPARSITY IN SOLVING OPTIMIZATION PROBLEMS  

Microsoft Academic Search

Exploiting sparsity has been a key issue in solving large-scale optimization pro blems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient matrix of the equation

Sunyoung Kim

246

Formulation of the multimission aircraft design optimization problem  

NASA Astrophysics Data System (ADS)

The conventional single-mission aircraft design optimization problem is reformulated to allow design and optimization for multiple missions. Defining the aircraft mission as a set of continuous scalar variables leads to the concepts of mission vector and mission space. The multimission aircraft design optimization problem becomes one of optimizing a design for several different points in the mission space, simultaneously. In the limit, a design can be optimized simultaneously for all points in the mission space. Mapping various points from the optimization design space into the mission space generates actual and theoretical optimum performance surfaces. The multimission optimum configuration is defined as the single configuration that minimizes the difference between the actual performance and the theoretical optimum performance. The multimission aircraft design optimization method can be applied over several distinct mission by summing the differences between actual and theoretical optimum performance, or over all possible missions by integrating the difference between the actual and theoretical optimum performance surfaces. The concepts associated with the mission vector, mission space, and multimission optimum configuration are presented in mathematical form. The objective function for the multimission optimization problem is expressed both as a summation over discrete mission points and as an integral over the entire mission space. Mathematical expressions for objective functions based on both single and multiple objectives are developed and presented. A weighting function, emphasizing certain parts of the mission space over others, is also discussed. The multimission aircraft design optimization method is applied to an elementary wing-design optimization problem for an executive jet. The optimization problem is solved numerically for single and multiple objectives, with and without a functional constraint. The effect of the different objective functions and the confounding effect of the mission-dependent functional constraint are discussed. The results obtained from the solution of the unconstrained wing-design optimization problem validates the multimission design optimization method in that the overall performance of the multimission optimum configurations is shown to exceed that of the configurations optimized for single missions. An aircraft performance model and numerical optimization code, which were developed for the present work, are also presented.

Straussfogel, Dennis M.

1998-12-01

247

Generalized Proximal Method for Efficient Solutions in Vector Optimization  

Microsoft Academic Search

This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed convex cone. In contrast to most published literature on this subject, our algorithm

T. D. Chuong

2011-01-01

248

Test problem construction for single-objective bilevel optimization.  

PubMed

In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included in the test problems independently of each other. In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels. As a companion to the test problem construction framework, the paper presents a standard test suite of 12 problems, which includes eight unconstrained and four constrained problems. Most of the problems are scalable in terms of variables and constraints. To provide baseline results, we have solved the proposed test problems using a nested bilevel evolutionary algorithm. The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm. The code related to the paper may be accessed from the website http://bilevel.org . PMID:24364674

Sinha, Ankur; Malo, Pekka; Deb, Kalyanmoy

2014-01-01

249

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

PubMed

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420

Josi?ski, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Swito?ski, Adam

2014-01-01

250

The Expanded Invasive Weed Optimization Metaheuristic for Solving Continuous and Discrete Optimization Problems  

PubMed Central

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420

Josi?ski, Henryk; Michalczuk, Agnieszka; ?wito?ski, Adam

2014-01-01

251

Forecasting Electricity Prices in an Optimization Hydrothermal Problem  

NASA Astrophysics Data System (ADS)

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

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

2007-12-01

252

An Evolutionary Approach to Combinatorial Optimization Problems  

E-print Network

working principles of genetic algorithms. Section 3 first presents our general principles for constructing of the genetic algorithm are re­ quired in order to achieve results of high quality even for the problem application of the genetic algorithm is observed to find the global opti­ mum within a number of runs

Khuri, Sami

253

SDP relaxations for some combinatorial optimization problems  

E-print Network

The space of p × q real matrices is denoted by Rp×q, the space of k × k symmetric ... generic model for various real-life problems, such as hospital layout [48, 27], balancing of .... In other words, to fix entry (r, s) in the permutation matrix X to one.

254

The quadratic interior point method solving power system optimization problems  

Microsoft Academic Search

Karmarkar's interior point method as a computation method for solving linear programming (LP) has attracted interest in the operation research community, due to its efficiency, reliability, and accuracy. This paper presents an extended quadratic interior point (EQIP) method, based on improvement of initial condition for solving both linear and quadratic programming problems, to solve power system optimization problem (PSOP), such

James A. Momoh; S. X. Guo; E. C. Ogbuobiri; R. Adapa

1994-01-01

255

Genetic Programming: Optimal Population Sizes for Varying Complexity Problems  

E-print Network

Genetic Programming: Optimal Population Sizes for Varying Complexity Problems Alan Piszcz and the ability to successfully evolve solutions. We find that population size sensitivity how much a genetic complex a problem is the more sensitive the genetic program's efficiency is to population size. Categories

Fernandez, Thomas

256

NEOS and Condor: solving optimization problems over the Internet  

Microsoft Academic Search

We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations

Michael C. Ferris; Michael P. Mesnier; Jorge J. Moré

2000-01-01

257

Design of Optimal Systolic Algorithms for the Transitive Closure Problem  

Microsoft Academic Search

New optimal systolic algorithms for the transitive closure problem on ring and linear arrays of processors is presented. The data dependency of the Warshal-Floyd algorithm is exploited to obtain highly pipelined parallel algorithms. One of the algorithms is asymptotically seven times more cost-effective than previous algorithms for computing transitive closure problems. The authors introduce a new expository device, called the

Dilip Sarkar; Amar Mukherjee

1992-01-01

258

Infinite Horizon Optimal Search Problem with Hiring and Firing Options  

E-print Network

of North Carolina at Charlotte, Department of Mathematics and Statistics, Char- lotte, NC 28223, USA. Email, marriage and divorce problem, entry and exit, sequential optimal stopping problem, invest and deinvest to study of social relationships, for example, marriages and divorces. For financial applications, repeat

Xu, Mingxin

259

Neural networks give a warm start to linear optimization problems  

Microsoft Academic Search

Hopfield neural networks and interior point methods are used in an integrated way to solve linear optimization problems. The neural network unveils a warm starting point for the primal-dual interior point method. This approach was applied to a set of real world linear programming problems. Results from a pure primal-dual algorithm provide a yardstick. The integrated approach provides promising results,

MARTA I. VELAZCO; A. R. L. Oliveira; CHRISTIANO LYRA

2002-01-01

260

Optimal Cost-Sharing Mechanisms for Steiner Forest Problems  

E-print Network

Optimal Cost-Sharing Mechanisms for Steiner Forest Problems Shuchi Chawla1 , Tim Roughgarden2 and groupstrategyproof mechanism for Steiner forest cost-sharing problems. We prove that this mechanism also achieves an O(log2 k)- approximation of the social cost, where k is the number of players. As a consequence

Roughgarden, Tim

261

Solving convex programs by random walks  

Microsoft Academic Search

In breakthrough developments about two decades ago, L. G. Khachiyan [14] showed that the Ellipsoid method solves linear programs in polynomial time, while M. Grötschel, L. Lovász and A. Schrijver [4, 5] extended this to the problem of minimizing a convex function over any convex set specified by a separation oracle. In 1996, P. M. Vaidya [21] improved the running

Dimitris Bertsimas; Santosh Vempala

2002-01-01

262

On optimal solution error covariances in variational data assimilation problems  

NASA Astrophysics Data System (ADS)

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection-diffusion model.

Gejadze, I. Yu.; Le Dimet, F.-X.; Shutyaev, V.

2010-03-01

263

Optimal Execution Problem for Geometric Ornstein-Uhlenbeck Price Process  

E-print Network

We study the optimal execution problem in the presence of market impact and give a generalization of the main result of Kato(2009). Then we consider an example where the security price follows a geometric Ornstein-Uhlenbeck process which has the so-called mean-reverting property, and then show that an optimal strategy is a mixture of initial/terminal block liquidation and intermediate gradual liquidation. When the security price has no volatility, the form of our optimal strategy is the same as results of Obizhaeva and Wang(2005) and Alfonsi et al.(2010), who studied the optimal execution in a limit-order-book model.

Kato, Takashi

2011-01-01

264

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

PubMed Central

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

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

2014-01-01

265

Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems  

NASA Technical Reports Server (NTRS)

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

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

2000-01-01

266

Sub-problem Optimization With Regression and Neural Network Approximators  

NASA Technical Reports Server (NTRS)

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

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

2003-01-01

267

Quadratic Kernelization for Convex Recoloring of Trees  

Microsoft Academic Search

The Convex Recoloring (CR) problem measures how far a tree of characters differs from exhibiting a so-called “perfect phylogeny”. For an input\\u000a consisting of a vertex-colored tree T, the problem is to determine whether recoloring at most k vertices can achieve a convex coloring, meaning by this a coloring where each color class induces a subtree. The problem\\u000a was introduced

Hans L. Bodlaender; Michael R. Fellows; Michael A. Langston; Mark A. Ragan; Frances A. Rosamond; Mark Weyer

268

Russian Doll Search for solving Constraint Optimization problems  

SciTech Connect

If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor quality of the lower bound on the global valuation of a partial assignment, even when using Forward Checking techniques. In this paper, we introduce the Russian Doll Search algorithm which replaces one search by n successive searches on nested subproblems (n being the number of problem variables), records the results of each search and uses them later, when solving larger subproblems, in order to improve the lower bound on the global valuation of any partial assignment. On small random problems and on large real scheduling problems, this algorithm yields surprisingly good results, which greatly improve as the problems get more constrained and the bandwidth of the used variable ordering diminishes.

Verfaillie, G.; Lemaitre, M. [CERT/ONERA, Toulouse (France); Schiex, T. [INRA, Castanet Tolosan (France)

1996-12-31

269

Application of neural networks in optimization problems: a review  

NASA Astrophysics Data System (ADS)

In the recent past neural networks have been used in a variety of applications. The wide spectrum of applications has required invention of new architectures as well as improving existing architectures. This paper reviews some of different neural network architectures and their applications in optimization problems. The paper is divided into three primary sections: 1) a brief review of the type of problems that are suitable for neural networks 2) a brief description of some of the more commonly used neural network models and 3) a quick glance at application of Hopfield network to optimization problems. The first part will provide a quick glance at the two class of problems best suited for neural networks. The second part will briefly review various networks currently in use today. The application section will provide examples describing use of Hopfield network for solving economic load dispatch and linear programming problems. The paper also includes an extensive bibliography. 1.

Ashenayi, Kaveh

1991-03-01

270

Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making  

Microsoft Academic Search

Natural basic concepts in multiple-objective optimization lead to difficult multiextremal global optimization problems. Examples include detection of efficient points when nonconvexities occur, and optimization of a linear function over the efficient set in the convex (even linear) case. Assuming that a utility function exists allows one to replace in general the multiple-objective program by a single, nonconvex optimization problem, which

R. Horst; N. V. Thoai

1997-01-01

271

A path following algorithm for the graph matching problem.  

PubMed

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art. PMID:19834143

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

2009-12-01

272

Overcoming the Bellman's curse of dimensionality in large optimization problems  

NASA Technical Reports Server (NTRS)

Decomposition of large problems into a hierarchic pyramid of subproblems was proposed in the literature as a means for optimization of engineering systems too large for all-in-one optimization. This decomposition was established heuristically. The dynamic programming (DP) method due to Bellman was augmented with an optimum sensitivity analysis that provides a mathematical basis for the above decomposition, and overcomes the curse of dimensionality that limited the original formulation of DP. Numerical examples are cited.

Sobieszczanski-Sobieski, Jaroslaw

1990-01-01

273

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

PubMed Central

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 ?0 minimization problem. Then, we relax this non-convex optimization to a convex ?1 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

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

2013-01-01

274

Quadratic Optimization in the Problems of Active Control of Sound  

NASA Technical Reports Server (NTRS)

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

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

2002-01-01

275

Numerical solution of some types of fractional optimal control problems.  

PubMed

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm "optimize first, then discretize" and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. PMID:24385874

Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H W

2013-01-01

276

A Discrete Lagrangian Algorithm for Optimal Routing Problems  

SciTech Connect

The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.

Kosmas, O. T.; Vlachos, D. S.; Simos, T. E. [University of Peloponnese, 22100 Tripoli (Greece)

2008-11-06

277

State-Constrained Optimal Control Problems of Impulsive Differential Equations  

SciTech Connect

The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.

Forcadel, Nicolas, E-mail: forcadel@ceremade.dauphine.fr [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail: Zhiping.Rao@ensta-paristech.fr; Zidani, Hasnaa, E-mail: Hasnaa.Zidani@ensta-paristech.fr [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)

2013-08-01

278

Approximating convex Pareto surfaces in multiobjective radiotherapy planning  

SciTech Connect

Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing.

Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R. [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114 (United States)

2006-09-15

279

Gearing optimization We consider an optimization problem that arises in machine-tool design. It  

E-print Network

Gearing optimization V.V. Lozin Abstract We consider an optimization problem that arises in machine. The edges of such a graph correspond to pairs of gear-wheels and the vertices stand for velocities this velocity by the central vertex of a star and call it the input vertex. By means of gear-wheels the rotation

Lozin, Vadim V.

280

Artificial Bee Colony Algorithm for Solving Optimal Power Flow Problem  

PubMed Central

This paper proposes an artificial bee colony (ABC) algorithm for solving optimal power flow (OPF) problem. The objective of the OPF problem is to minimize total cost of thermal units while satisfying the unit and system constraints such as generator capacity limits, power balance, line flow limits, bus voltages limits, and transformer tap settings limits. The ABC algorithm is an optimization method inspired from the foraging behavior of honey bees. The proposed algorithm has been tested on the IEEE 30-bus, 57-bus, and 118-bus systems. The numerical results have indicated that the proposed algorithm can find high quality solution for the problem in a fast manner via the result comparisons with other methods in the literature. Therefore, the proposed ABC algorithm can be a favorable method for solving the OPF problem. PMID:24470790

Le Dinh, Luong; Vo Ngoc, Dieu

2013-01-01

281

Artificial bee colony algorithm for solving optimal power flow problem.  

PubMed

This paper proposes an artificial bee colony (ABC) algorithm for solving optimal power flow (OPF) problem. The objective of the OPF problem is to minimize total cost of thermal units while satisfying the unit and system constraints such as generator capacity limits, power balance, line flow limits, bus voltages limits, and transformer tap settings limits. The ABC algorithm is an optimization method inspired from the foraging behavior of honey bees. The proposed algorithm has been tested on the IEEE 30-bus, 57-bus, and 118-bus systems. The numerical results have indicated that the proposed algorithm can find high quality solution for the problem in a fast manner via the result comparisons with other methods in the literature. Therefore, the proposed ABC algorithm can be a favorable method for solving the OPF problem. PMID:24470790

Le Dinh, Luong; Vo Ngoc, Dieu; Vasant, Pandian

2013-01-01

282

An optimized finite-difference scheme for wave propagation problems  

NASA Technical Reports Server (NTRS)

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.; Lomax, H.; Jurgens, H.

1993-01-01

283

On Optimal AMLI Solvers for Incompressible Navier-Stokes Problems  

NASA Astrophysics Data System (ADS)

We consider the incompressible Navier-Stokes problem and a projection scheme based on Crouzeix-Raviart finite element approximation of the velocities and piece-wise constant approximation of the pressure. These non-conforming finite elements guarantee that the divergence of the velocity field is zero inside each element, i.e., the approximation is locally conservative. We propose optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners for both, the decoupled scalar parabolic problems at the prediction step as well as to the mixed finite element method (FEM) problem at the projection step. The main contribution of the current paper is the obtained scalability of the AMLI methods for the related composite time-stepping solution method. The algorithm for the Navier-Stokes problem has a total computational complexity of optimal order. We present numerical tests for the efficiency of the AMLI solvers for the case of lid-driven cavity flow for different Reynolds numbers.

Boyanova, P.; Margenov, S.

2010-11-01

284

On destination optimality in asymmetric distance Fermat-Weber problems  

Microsoft Academic Search

This paper introduces skewed norms, i.e. norms perturbed by a linear function, which are useful for modelling asymmetric distance\\u000a measures. The Fermat-Weber problem with mixed skewed norms is then considered. Using subdifferential calculus we derive exact\\u000a conditions for a destination point to be optimal, thereby correcting and completing some recent work on asymmetric distance\\u000a location problems. Finally the classical dominance

Frank Plastria

1992-01-01

285

Convex Models of Distribution System Reconfiguration  

E-print Network

We derive new mixed-integer quadratic, quadratically constrained, and second-order cone programming models of distribution system reconfiguration, which are to date the first formulations of the ac problem that have convex, ...

Taylor, Joshua A.

286

The Blocking Numbers of Convex Bodies  

Microsoft Academic Search

.    Besides determining the exact blocking numbers of cubes and balls, a conditional lower bound for the blocking numbers of\\u000a convex bodies is achieved. In addition, several open problems are proposed.

L. Dalla; David G. Larman; Peter Mani-levitska; Chuanming Zong

2000-01-01

287

A teaching learning based optimization based on orthogonal design for solving global optimization problems.  

PubMed

In searching for optimal solutions, teaching learning based optimization (TLBO) (Rao et al. 2011a; Rao et al. 2012; Rao & Savsani 2012a) algorithms, has been shown powerful. This paper presents an, improved version of TLBO algorithm based on orthogonal design, and we call it OTLBO (Orthogonal Teaching Learning Based Optimization). OTLBO makes TLBO faster and more robust. It uses orthogonal design and generates an optimal offspring by a statistical optimal method. A new selection strategy is applied to decrease the number of generations and make the algorithm converge faster. We evaluate OTLBO to solve some benchmark function optimization problems with a large number of local minima. Simulations indicate that OTLBO is able to find the near-optimal solutions in all cases. Compared to other state-of-the-art evolutionary algorithms, OTLBO performs significantly better in terms of the quality, speed, and stability of the final solutions. PMID:23875125

Satapathy, Suresh Chandra; Naik, Anima; Parvathi, K

2013-12-01

288

A New Local Search Based Ant Colony Optimization Algorithm for Solving Combinatorial Optimization Problems  

NASA Astrophysics Data System (ADS)

Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.

Hassan, Md. Rakib; Islam, Md. Monirul; Murase, Kazuyuki

289

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

PubMed

The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance. PMID:25008005

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

2014-09-01

290

On String-Averaging for Sparse Problems and On the Split Common ...  

E-print Network

Institutes of Health (NIH) grant No. ... erations Research 26 (2001), 248—264. [7] H.H. ... cal specimens by electron microscopy, Proceedings of The International ... methods for convex feasibility and optimization problems, IEEE Journal.

User

2008-10-07

291

A Dynamic Programming Framework for Combinatorial Optimization Problems on  

E-print Network

A Dynamic Programming Framework for Combinatorial Optimization Problems on Graphs with Bounded's performance and fault tolerance. The main technique considered in this paper is dynamic programming. I in the rest of the paper. In Section III we present a generic dynamic programming framework for solving combi

Paris-Sud XI, Université de

292

To the optimization problem in minority game model  

SciTech Connect

The article presents the research results of the optimization problem in minority game model to a gaussian approximation using replica symmetry breaking by one step (1RSB). A comparison to replica symmetry approximation (RS) and the results from literary sources received using other methods has been held.

Yanishevsky, Vasyl [Drogobych Ivan Franko University, 36 Ivan Franko St., 82100 (Ukraine)

2009-12-14

293

Towards Grid Implementations of Metaheuristics for Hard Combinatorial Optimization Problems  

Microsoft Academic Search

Metaheuristics are approximation algorithms that nd very good solutions to hard combinatorial optimization problems at the expense of large computational require- ments. They do, however, offer a wide range of possibili- ties for implementations of effective robust parallel algo- rithms which run in much smaller computation times. We present four strategies for the parallelization of an extended GRASP with ILS

Cristina Boeres; Vinod E. F. Rebello; Celso C. Ribeiro

294

Towards Grid Implementations of Metaheuristics for Hard Combinatorial Optimization Problems  

Microsoft Academic Search

Metaheuristics are approximate algorithms that are able to find very good solutions to hard combinatorial optimization problems. They do, however, offer a wide range of possibilities for implementations of effective robust parallel algorithms which run in much smaller computation times than their sequential counterparts. We present four slightly differing strategies for the parallelization of an extended GRASP with ILS heuristic

Aletia Patrícia Favacho De Araujo; Sebastian Urrutia; Cristina Boeres; Vinod E. F. Rebello; Celso C. Ribeiro

2005-01-01

295

Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization \\Lambda  

E-print Network

trillion standard cubic feet of natural gas per year, representing roughly a third of worldwide consumption consider minimization of the cost of fuel and/or electric power for the compressor stations in a gasAlgorithms for Noisy Problems in Gas Transmission Pipeline Optimization \\Lambda R. G. Carter y J. M

296

Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization  

E-print Network

trillion standard cubic feet of natural gas per year, representing roughly a third of worldwide consumption minimization of the cost of fuel and/or electric power for the compressor stations in a gas pipeline networkAlgorithms for Noisy Problems in Gas Transmission Pipeline Optimization R. G. Cartery J. M

297

LU TP 9211 Neural Networks for Optimization Problems with  

E-print Network

March 1992 LU TP 92­11 Neural Networks for Optimization Problems with Inequality Constraints using mean field neural networks is presented. The constraints x Ÿ 0 are encoded by x\\Theta(x) terms this is computationally possible (N Ÿ 30). The quality of the neural network solutions consistently lies above 95

Peterson, Carsten

298

Intelligent evolutionary algorithms for large parameter optimization problems  

Microsoft Academic Search

This work proposes two intelligent evolutionary algorithms IEA and IMOEA using a novel intelligent gene collector (IGC) to solve single and multiobjective large parameter optimization problems, respectively. IGC is the main phase in an intelligent recombination operator of IEA and IMOEA. Based on orthogonal experimental design, IGC uses a divide-and-conquer approach, which consists of adaptively dividing two individuals of parents

Shinn-ying Ho; Li-sun Shu; Jian-hung Chen

2004-01-01

299

Cores of convex games  

Microsoft Academic Search

The core of ann-person game is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one that is based on a convex set function. In this paper it is shown that the core of a convex game is not empty and that it has an especially regular structure.

Lloyd S. Shapley

1971-01-01

300

Near-optimal deterministic algorithms for volume computation via M-ellipsoids  

PubMed Central

We give a deterministic algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This leads to a nearly optimal deterministic algorithm for estimating the volume of a convex body and improved deterministic algorithms for fundamental lattice problems under general norms.

Dadush, Daniel; Vempala, Santosh S.

2013-01-01

301

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method  

NASA Astrophysics Data System (ADS)

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

Vasant, Pandian

2011-06-01

302

Solving the minimum labelling spanning tree problem using intelligent optimization  

E-print Network

Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the MLST problem has been shown to be NP-hard and some effective heuristics have been proposed and analyzed. In this paper we present an intelligent optimization algorithm to solve the problem. It is obtained by the basic Variable Neighbourhood Search heuristic with the integration of other complements from machine learning, statistics and experimental algorithmics, in order to produce high-quality performance and to completely automate the resulting optimization strategy. We present experimental results on randomly generated graphs with different statistical properties, showing the crucial effects of the implementation, the robustness, and the empirical scalability of our intelligent algorithm. Furthermore, the computational experiments show that the proposed strategy outperfor...

Consoli, Sergio; Moreno-Perez, Jose Andres

2012-01-01

303

Statistical physics of hard combinatorial optimization: Vertex cover problem  

NASA Astrophysics Data System (ADS)

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

304

Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem  

SciTech Connect

We consider a virtual power plant, which is given the task of dispatching a fluctuating power supply to a portfolio of flexible consumers. The flexible consumers are modeled as discrete batch processes, and the associated optimization problem is denoted the discrete virtual power plant dispatch problem (DVPPDP). First, the nondeterministic polynomial time (NP)-completeness of the discrete virtual power plant dispatch problem is proved formally. We then proceed to develop tailored versions of the meta-heuristic algorithms hill climber and greedy randomized adaptive search procedure (GRASP). The algorithms are tuned and tested on portfolios of varying sizes. We find that all the tailored algorithms perform satisfactorily in the sense that they are able to find sub-optimal, but usable, solutions to very large problems (on the order of 105 units) at computation times on the scale of just 10 s, which is far beyond the capabilities of the optimal algorithms we have tested. In particular, GRASP sorted shows with the most promising performance, as it is able to find solutions that are both agile (sorted) and well balanced, and consistently yields the best numerical performance among the developed algorithms.

Petersen, Mette K.; Hansen, Lars H.; Bendtsen, Jan; Edlund, Kristian; Stoustrup, Jakob

2014-10-17

305

The 2-D magnetotelluric inverse problem solved with optimization  

NASA Astrophysics Data System (ADS)

The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

van Beusekom, Ashley E.; Parker, Robert L.; Bank, Randolph E.; Gill, Philip E.; Constable, Steven

2011-02-01

306

Multiresolution strategies for the numerical solution of optimal control problems  

NASA Astrophysics Data System (ADS)

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

Jain, Sachin

307

Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization  

Microsoft Academic Search

We observe that in a simple one-dimensional polynomial optimization problem (POP), the `optimal' values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Some pieces of circumstantial evidences for the strange behaviours

M. Nakata; M. Muramatsu; H. Waki

2010-01-01

308

Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization  

Microsoft Academic Search

We observe that in a simple one-dimensional polynomial optimization problem (POP), the `optimal' values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Some pieces of circumstantial evidences for the strange behaviours

M. Nakata; M. Muramatsu; H. Waki

2008-01-01

309

An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems  

Microsoft Academic Search

Scheduling for the flexible job-shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. Particle swarm optimization is an evolutionary computation technique

Weijun Xia; Zhiming Wu

2005-01-01

310

Application of data-driven design optimization methodology to a multi-objective design optimization problem  

Microsoft Academic Search

The data-driven design optimization methodology (DDDOM) is an application of the dynamic data-driven application system concept in the engineering design domain. The DDDOM combines experiments and simulations concurrently and tends to achieve better designs in less time with less effort than traditional methods. This paper presents the application of the DDDOM to a multi-objective design optimization problem—design of a cooling

H. Zhao; T. Icoz; Y. Jaluria; D. Knight

2007-01-01

311

Convex optimization for multi-class image labeling with a novel family of total variation based regularizers  

Microsoft Academic Search

We introduce a linearly weighted variant of the total variation for vector fields in order to formulate regularizers for multi-class labeling problems with non-trivial interclass distances. We characterize the possible distances, show that Euclidean distances can be exactly represented, and review some methods to approximate non-Euclidean distances in order to define novel total variation based regularizers. We show that the

Jan Lellmann; Florian Becker; Christoph Schnörr

2009-01-01

312

Optimal least-squares finite element method for elliptic problems  

NASA Technical Reports Server (NTRS)

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

313

Radio interferometric gain calibration as a complex optimization problem  

E-print Network

Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as StefCal and peeling can be understood...

Smirnov, Oleg

2015-01-01

314

Performance of quantum annealing in solving optimization problems: A review  

NASA Astrophysics Data System (ADS)

Quantum annealing is one of the optimization method for generic optimization problems. It uses quantum mechanics and is implemented by a quantum computer ideally. At the earlier stage, several numerical experiments using conventional computers have provided results showing that quantum annealing produces an answer faster than simulated annealing, a classical counterpart of quantum annealing. Later, theoretical and numerical studies have shown that there are drawbacks in quantum annealing. The power of quantum annealing is still an open problem. What makes quantum annealing a hot topic now is that a quantum computer based on quantum annealing is manufactured and commercialized by a Canadian company named D-Wave Systems. In the present article, we review the study of quantum annealing, focusing mainly on its power.

Suzuki, S.

2015-02-01

315

A Distributed Optimization Approach to Constrained OSNR Problem  

Microsoft Academic Search

This paper studies constrained optical signal-to-noise ratio (OSNR) problem via a distributed optimization approach. In multi-channel optical systems, the signal over an optical link can be regarded as an interfering noise for others, which leads to OSNR degradation. Regulating the input optical power at the Source (transmitter) aims to achieve satisfactory OSNR level at the Destination (receiver) for each channel.

Yan Pan; Tansu Alpcan; Lacra Pavel

2008-01-01

316

Optimization of Order Fulfillment in Distribution Network Problems  

Microsoft Academic Search

This paper focuses on optimization of order due date fulfillment reliability in multi-echelon distribution network problems\\u000a with uncertainties present in the production lead time, transportation lead time, and due date of orders. Reliability regarding\\u000a order due date fulfillment is critical in customer service, and customer retention. However, this reliability can be seriously\\u000a influenced by supply chain uncertainties, which may induce

Felix T. S. Chan; S. H. Chung; K. L. Choy

2006-01-01

317

The optimal cordon-based network congestion pricing problem  

Microsoft Academic Search

This paper investigates the cordon-based second-best congestion-pricing problems on road networks, including optimal selection of both toll levels and toll locations. A road network is viewed as a directed graph and the cutset concept in graph theory is used to describe the mathematical properties of a toll cordon by examining the incidence matrix of the network. Maximization of social welfare

Xiaoning Zhang; Hai Yang

2004-01-01

318

Optimal Control and the Aircraft Radar Evasion Problem  

Microsoft Academic Search

This paper considers the problem of optimal path planning for unmanned aerial vehicles in the presence of radar-guided surface-to-air missiles. The goal is to generate trajectories that ensure that the aerial vehicle visit a given set of way points while avoiding a given set of known locations of radar units. In this paper we first discuss the general radar evasion

I. I. Hussein; F. H. Zeitz; A. M. Bloch

2007-01-01

319

Parent-centric differential evolution algorithm for global optimization problems  

Microsoft Academic Search

Differential evolution (DE) is a population based evolutionary search algorithm widely used for solving optimization problems.\\u000a In the present article we investigate the application of parent-centric approach on the performance of classical DE, without\\u000a tampering with the basic structure of DE. The parent-centric approach is embedded in the mutation phase of DE. We propose\\u000a two versions of (DE) called differential

Millie Pant; Musrrat Ali; V. P. Singh

2009-01-01

320

New Variants of Genetic Algorithms Applied to Problems of Combinatorial Optimization  

Microsoft Academic Search

Problems of Combinatorial Optimization distinguish themselves by their well-structured problem description as well as by their huge number of possible action alternatives. Especially in the area of production and operational logistics these problems frequently occur. Their advantage lies in their subjective understanding of action alternatives and their objective functions. The use of classical optimization methods for problems of combinatorial optimization

Michael Afienzeller

321

AN INTERIOR POINT ALGORITHM FOR SOLVING LINEAR OPTIMIZATION OVER THE EFFICIENT SET PROBLEMS  

Microsoft Academic Search

The efficient set of a multiple objective linear programming problem is usually nonconvex, hence linear optimization over the efficient set problem is classified as a nonlinear optimization problem. This paper presents a modified interior point algorithm for solving linear optimization over the efficient set problems. Using computational experiments, we show that the modified algorithm provides an effective and accurate approach

Wei-Tai Weng; Ue-Pyng Wen

2001-01-01

322

CONVEX HULL RELAXATION (CHR) FOR CONVEX AND ...  

E-print Network

relaxation without separating any constraint, i.e., of defining the convex hull relaxation (CHR) ..... The experiments were done over a couple of years, and we always ... Ahlatç?o?lu, A., (2007) summer paper, OPIM Dept., Univ. of Pennsylvania.

HP_Administrator

2011-01-30

323

Issues and Strategies in Solving Multidisciplinary Optimization Problems  

NASA Technical Reports Server (NTRS)

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya

2013-01-01

324

Solving topology optimization problems by the Guide-Weight method  

NASA Astrophysics Data System (ADS)

Finding a good solution method for topology optimization problems is always paid attention to by the research field because they are subject to the large number of the design variables and to the complexity that occurs because the objective and constraint functions are usually implicit with respect to design variables. Guide-Weight method, proposed first by Chen in 1980s, was effectively and successfully used in antenna structures' optimization. This paper makes some improvement to it so that it possesses the characteristics of both the optimality criteria methods and the mathematical programming methods. When the Guide-Weight method is applied into topology optimization, it works very well with unified and simple form, wide availability and fast convergence. The algorithm of the Guide-Weight method and the improvement on it are described; two formulations of topology optimization solved by the Guide-Weight method combining with SIMP method are presented; subsequently, three numerical examples are provided, and comparison of the Guide-Weight method with other methods is made.

Liu, Xinjun; Li, Zhidong; Wang, Liping; Wang, Jinsong

2011-03-01

325

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

NASA Astrophysics Data System (ADS)

For both the conventional radio frequency and the comparably recent optical wireless communication systems, extensive effort from the academia had been made in improving the network spectrum efficiency and/or reducing the error rate. To achieve these goals, many fundamental challenges such as power efficient constellation design, nonlinear distortion mitigation, channel training design, network scheduling and etc. need to be properly addressed. In this dissertation, novel schemes are proposed accordingly to deal with specific problems falling in category of these challenges. Rigorous proofs and analyses are provided for each of our work to make a fair comparison with the corresponding peer works to clearly demonstrate the advantages. The first part of this dissertation considers a multi-carrier optical wireless system employing intensity modulation (IM) and direct detection (DD). A block-wise constellation design is presented, which treats the DC-bias that conventionally used solely for biasing purpose as an information basis. Our scheme, we term it MSM-JDCM, takes advantage of the compactness of sphere packing in a higher dimensional space, and in turn power efficient constellations are obtained by solving an advanced convex optimization problem. Besides the significant power gains, the MSM-JDCM has many other merits such as being capable of mitigating nonlinear distortion by including a peak-to-power ratio (PAPR) constraint, minimizing inter-symbol-interference (ISI) caused by frequency-selective fading with a novel precoder designed and embedded, and further reducing the bit-error-rate (BER) by combining with an optimized labeling scheme. The second part addresses several optimization problems in a multi-color visible light communication system, including power efficient constellation design, joint pre-equalizer and constellation design, and modeling of different structured channels with cross-talks. Our novel constellation design scheme, termed CSK-Advanced, is compared with the conventional decoupled system with the same spectrum efficiency to demonstrate the power efficiency. Crucial lighting requirements are included as optimization constraints. To control non-linear distortion, the optical peak-to-average-power ratio (PAPR) of LEDs can be individually constrained. With a SVD-based pre-equalizer designed and employed, our scheme can achieve lower BER than counterparts applying zero-forcing (ZF) or linear minimum-mean-squared-error (LMMSE) based post-equalizers. Besides, a binary switching algorithm (BSA) is applied to improve BER performance. The third part looks into a problem of two-phase channel estimation in a relayed wireless network. The channel estimates in every phase are obtained by the linear minimum mean squared error (LMMSE) method. Inaccurate estimate of the relay to destination (RtD) channel in phase 1 could affect estimate of the source to relay (StR) channel in phase 2, which is made erroneous. We first derive a close-form expression for the averaged Bayesian mean-square estimation error (ABMSE) for both phase estimates in terms of the length of source and relay training slots, based on which an iterative searching algorithm is then proposed that optimally allocates training slots to the two phases such that estimation errors are balanced. Analysis shows how the ABMSE of the StD channel estimation varies with the lengths of relay training and source training slots, the relay amplification gain, and the channel prior information respectively. The last part deals with a transmission scheduling problem in a uplink multiple-input-multiple-output (MIMO) wireless network. Code division multiple access (CDMA) is assumed as a multiple access scheme and pseudo-random codes are employed for different users. We consider a heavy traffic scenario, in which each user always has packets to transmit in the scheduled time slots. If the relay is scheduled for transmission together with users, then it operates in a full-duplex mode, where the packets previously collected from users are transmitted to the destination

Gao, Qian

326

CONVEX mini manual  

NASA Technical Reports Server (NTRS)

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.

Tennille, Geoffrey M.; Howser, Lona M.

1993-01-01

327

A self-learning particle swarm optimizer for global optimization problems.  

PubMed

Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms. PMID:22067435

Li, Changhe; Yang, Shengxiang; Nguyen, Trung Thanh

2012-06-01

328

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

SciTech Connect

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

Kmet', Tibor [Department of Informatics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra (Slovakia); Kmet'ova, Maria [Department of Mathematics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra (Slovakia)

2009-09-09

329

Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control Problems  

E-print Network

Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control Problems on Graduate Students #12;[This page intentionally left blank.] #12;Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control Problems by Geoffrey Todd Huntington Author

330

Multi-objective evolutionary methods for time-changing portfolio optimization problems  

E-print Network

This thesis is focused on the discovery of efficient asset allocations with the use of evolutionary algorithms. The portfolio optimization problem is a multi-objective optimization problem for the conflicting criteria of ...

Hatzakis, Iason

2007-01-01

331

A mathematical programming approach to stochastic and dynamic optimization problems  

SciTech Connect

We propose three ideas for constructing optimal or near-optimal policies: (1) for systems for which we have an exact characterization of the performance space we outline an adaptive greedy algorithm that gives rise to indexing policies (we illustrate this technique in the context of indexable systems); (2) we use integer programming to construct policies from the underlying descriptions of the performance space (we illustrate this technique in the context of polling systems); (3) we use linear control over polyhedral regions to solve deterministic versions for this class of problems. This approach gives interesting insights for the structure of the optimal policy (we illustrate this idea in the context of multiclass queueing networks). The unifying theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic and dynamic optimization parallels efforts of the mathematical programming community in the last fifteen years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and new algorithms with provable a posteriori guarantees for their suboptimality for polling systems, multiclass queueing and loss networks.

Bertsimas, D.

1994-12-31

332

On the robust optimization to the uncertain vaccination strategy problem  

SciTech Connect

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id [Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran Indonesia, Jalan Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 (Indonesia)

2014-02-21

333

On the robust optimization to the uncertain vaccination strategy problem  

NASA Astrophysics Data System (ADS)

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

Chaerani, D.; Anggriani, N.; Firdaniza

2014-02-01

334

A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming  

Microsoft Academic Search

This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally

Arjan Berkelaar; Joaquim A. S. Gromicho; Roy Kouwenberg; Shuzhong Zhang

2005-01-01

335

New attitude penalty functions for spacecraft optimal control problems  

SciTech Connect

A solution of a spacecraft optimal control problem, whose cost function relies on an attitude description, usually depends on the choice of attitude coordinates used. A problem could be solved using 3-2-1 Euler angles or using classical Rodriguez parameters and yield two different ``optimal`` solutions, unless the performance index in invariant with respect to the attitude coordinate choice. Another problem arising with many attitude coordinates is that they have no sense of when a body has tumbled beyond 180{degrees} from the reference attitude. In many such cases it would be easier (i.e. cost less) to let the body complete the revolution than to force it to reverse the rotation and return to the desired attitude. This paper develops a universal attitude penalty function g() whose value is independent of the attitude coordinates chosen to represent it. Furthermore, this function will achieve its maximum value only when a principal rotation of {plus_minus}180{degrees} from the target state is performed. This will implicitly permit the g() function to sense the shortest rotational distance back to the reference state. An attitude penalty function which depends on the Modified Rodriguez Parameters (MRP) will also be presented. These recently discovered MRPs are a non-singular three-parameter set which can describe any three-attitude. This MRP penalty function is simpler than the attitude coordinate independent g() function, but retains the useful property of avoiding lengthy principal rotations of more than {plus_minus}180{degrees}.

Schaub, H.; Junkins, J.L. [Texas A and M Univ., College Station, TX (United States). Dept. of Aerospace Engineering; Robinett, R.D. [Sandia National Labs., Albuquerque, NM (United States)

1996-03-01

336

Grouping-based evolutionary algorithm: seeking balance between feasible and infeasible individuals of constrained optimization problems  

Microsoft Academic Search

Most of the optimization problems in the real world have constraints. In recent years, evolutionary algorithms caught a lot of researchers' attention for solving constrained optimization problems. Infeasible individuals are often underrated by most of the current evolutionary algorithms when evolutionary algorithms are used for solving constraint optimization problems. This paper proposes an approach to balance the feasible and infeasible

Ming Yuchi; Jong-Hwan Kim

2004-01-01

337

From Genes to Memes: Optimization by Problem-aware Evolutionary Algorithms  

Microsoft Academic Search

Memetic algorithms are population-based metaheuristics aimed to solve hard optimization problems. These techniques are explic- itly concerned with exploiting available knowledge in order to achieve the most effective resolution of the target problem. The rationale be- hind this optimization philosophy, namely the intrinsic theoretical limi- tations of problem-unaware optimization techniques, is presented in this work. A glimpse of the main

Carlos Cotta

338

Solving Large Scale Optimization Problems via Grid and Cluster Computing 1  

Microsoft Academic Search

Solving large scale optimization problems requires a huge amount of computational power. The size of optimization problems that can be solved on a few CPUs has been lim- ited due to a lack of computational power. Grid and cluster computing has received much attention as a powerful and inexpensive way of solving large scale optimization problems that an existing single-unit

Katsuki Fujisawa; Masakazu Kojima; Akiko Takeda; Makoto Yamashita

2003-01-01

339

A convex lateral tibial plateau for knee replacement  

Microsoft Academic Search

Unicompartmental knee replacements have not performed as well in the lateral compartment as in the medial. This may be because the tibial components have flat or slightly concave surfaces which match the medial plateau but not the convex lateral plateau. The aim of this study was to find the optimal radius for a convex lateral tibial component.Twelve normal lateral tibial

J. V. Baré; H. S. Gill; D. J. Beard; D. W. Murray

2006-01-01

340

The extremal volume ellipsoids of convex bodies, their symmetry ...  

E-print Network

symmetric convex body K is the unit ball of a Banach space, and if K is an ellipsoid, then the Banach ...... 371–418. [31] Polyak, B. T. Convexity of quadratic transformations and its use in control and ... Optim. 17, 3 (2006), 621–641 (

2007-09-05

341

On several results about convex set functions  

NASA Astrophysics Data System (ADS)

In 1979, in an interesting paper, R.J. Morris introduced the notion of convex set function defined on an atomless finite measure space. After a short period this notion, as well as generalizations of it, began to be studied in several papers. The aim was to obtain results similar to those known for usual convex (or generalized convex) functions. Unfortunately several notions are ambiguous and the arguments used in the proofs of several results are not clear or not correct. In this way there were stated even false results. The aim of this paper is to point out that using some simple ideas it is possible, on one hand, to deduce the correct results by means of convex analysis and, on the other hand, to emphasize the reasons for which there are problems with other results.

Zalinescu, C.

2007-04-01

342

Finite element solution of optimal control problems with inequality constraints  

NASA Technical Reports Server (NTRS)

A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

Bless, Robert R.; Hodges, Dewey H.

1990-01-01

343

Algorithms for bilevel optimization  

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

344

Greedy approximation in convex optimization  

E-print Network

Jun 2, 2012 ... linear combinations of elements from a given system (dictionary) is ... a certain functional determined by information from the previous steps of ... (choosing coefficients of the linear combination) the m-term approximant.

2012-06-02

345

Convexity recognition of the union of polyhedra  

Microsoft Academic Search

In this paper we consider the following basic problem in polyhedral computation: Given two polyhedra in Rd, P and Q, decide whether their union is convex, and, if so, compute it. We consider the three natural specializations of the problem: (1) when the polyhedra are given by halfspaces (H-polyhedra), (2) when they are given by vertices and extreme rays (V-polyhedra),

Alberto Bemporad; Komei Fukuda; Fabio Danilo Torrisi

2001-01-01

346

Abstract Convexity, Some Relations and Applications  

Microsoft Academic Search

The aim of this article is to analyze the relationship between various notions of abstract convexity structures that we find in the literature, in connection with the problem of the existence of continuous selections and fixed points of correspondences. We focus mainly on the notion of mc -spaces, which was introduced in [J.V. LLinares (1998). Unified treatment of the problem

Juan-Vicente Llinares

2002-01-01

347

A genetic algorithm approach to large scale combinatorial optimization problems in the advertising industry  

Microsoft Academic Search

The effectiveness of applying genetic algorithms to combinatorial optimization has been widely demonstrated using many types of benchmark problems, such as the traveling salesman problems and job-shop scheduling problems. We want to optimize strategies for advertising in newspapers sold in Japan. Our problem is to select appropriate newspapers and find the correct frequency of advertising for a product in order

Kazuhiro Ohkura; Takashi Igarashi; Kaqji Ueda; S. Okauchi; H. Matsunaga

2001-01-01

348

Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions  

E-print Network

Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions Kevin for understanding the algorithm-specific empirical hardness of NP-Hard problems. In this work we focus on the empirical hardness of the winner determination problem--an optimization problem arising in combinatorial

Shoham, Yoav

349

Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions  

E-print Network

Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions Kevin for understanding the algorithm­specific empirical hardness of NP­Hard problems. In this work we focus on the empirical hardness of the winner determination problem---an optimization problem arising in combinatorial

Shoham, Yoav

350

Optimal placement of FACTS devices for multi-objective voltage stability problem  

Microsoft Academic Search

In this paper, a new method for optimal locating multi-type FACTS devices in order to optimize multi-objective voltage stability problem is presented. The proposed methodology is based on a new variant of Particle Swarm Optimization (PSO) specialized in multi-objective optimization problem known as Non-dominated Sorting Particle Swarm Optimization (NSPSO). The crowding distance technique is used to maintain the Pareto front

R. Benabid; M. Boudour; M. A. Abido

2009-01-01

351

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

PubMed

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. PMID:23777526

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

2013-10-01

352

a block coordinate descent method for regularized multi-convex ...  

E-print Network

This paper considers regularized block multi-convex optimization, where the feasible set and ...... For example, the sparse logistic regression function ...... [61] RWH Sargent and DJ Sebastian, On the convergence of sequential minimization

2012-09-07

353

Optimal Control Problem of Feeding Adaptations of Daphnia and Neural Network Simulation  

NASA Astrophysics Data System (ADS)

A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints and open final time. The optimal control problem is transcribed into nonlinear programming problem, which is implemented with adaptive critic neural network [9] and recurrent neural network for solving nonlinear proprojection equations [10]. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach and neural network solving of nonlinear equations hold promise for obtaining the optimal control with control and state constraints and open final time.

Kmet', Tibor; Kmet'ov, Mria

2010-09-01

354

A relaxed reduced space SQP strategy for dynamic optimization problems.  

SciTech Connect

Recently, strategies have been developed to solve dynamic simulation and optimization problems in a simultaneous manner by applying orthogonal collocation on finite elements and solving the nonlinear program (NLP) with a reduced space successive quadratic programming (SQP) approach. We develop a relaxed simultaneous approach that leads to faster performance. The method operates in the reduced space of the control variables and solves the collocation equations inexactly at each SQP iteration. Unlike previous simultaneous formulations, it is able to consider the state variables one element at a time. Also, this approach is compared on two process examples to the reduced gradient, feasible path approach outlined in Logsdon and Biegler. Nonlinear programs with up to 5500 variables are solved with only 40% of the effort. Finally, a theoretical analysis of this approach is provided.

Logsdon, J. S.; Biegler, L. T.; Carnegie-Mellon Univ.

1993-01-01

355

Human opinion dynamics: an inspiration to solve complex optimization problems.  

PubMed

Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making. PMID:24141795

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P; Kapur, Pawan

2013-01-01

356

One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics  

SciTech Connect

We study the existence of optimal solutions for a class of infinite horizon nonconvex autonomous discrete-time optimal control problems. This class contains optimal control problems without discounting arising in economic dynamics which describe a model with a nonconcave utility function.

Zaslavski, Alexander J., E-mail: ajzasl@tx.technion.ac.il [Technion-Israel Institute of Technology, Department of Mathematics (Israel)

2011-12-15

357

Concepts of Aspect-Oriented Modeling Applied to Optimal Power Flow Problems  

Microsoft Academic Search

Optimization of complex systems demands advanced methods that are implemented in specialized software. Multiple combinations of optimization methods, objective functions, and constraints further complicate the problem of developing this software, making it hard to create, maintain, and evolve. To overcome this problem, this paper presents a new development methodology based on ideas of aspect-oriented programming (AOP) applied to optimal power

Daniele A. Barbosa; Leonardo M. Honório; Armando M. Leite da Silva; C. V. Lopes

2009-01-01

358

Chance-Constrained Guidance With Non-Convex Constraints  

NASA Technical Reports Server (NTRS)

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

Ono, Masahiro

2011-01-01

359

A sparse superlinearly convergent SQP with applications to two-dimensional shape optimization.  

SciTech Connect

Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show that, for a very large class of optimization problems, one can design SQP algorithms that satisfy all these three requirements. The improvements in computational efficiency are demonstrated for a cam design problem.

Anitescu, M.

1998-04-15

360

Nonlinear weighted multiple centrality corrections interior point method for optimal power flow  

Microsoft Academic Search

Optimal power flow (OPF) is a large scale nonlinear non-convex optimization problem. In the last decades many algorithms are developed to solve these problems and the interior point method (IPM) is a popular one. The primal-dual IPMs and their later developments have attracted much research interest. Impressed by the improvements in convergent performance of the further developed multiple centrality corrections

Zhiguang Huang; Quanyuan Jiang

2009-01-01

361

Stochastic Methods for Hard Stochastic Methods for Hard Stochastic Methods for Hard Stochastic Methods for Hard Optimization. Application to Robust Optimization. Application to Robust Optimization. Application to Robust Optimization. Application to Robust Fault Diagnosis and Control of Fault Diagnosis and Control of Fault Diagnosis and Control of Fault Diagnosis and Control of Industrial Systems Industrial Systems Industrial Systems Industrial Systems  

Microsoft Academic Search

This chapter aims at solving difficult optimizatio n problems arising in many engineering areas. To this end, a brief review of the main stochastic methods which can be used for solving continuous non- convex constrained optimization problems is present ed i.e.: Simulated annealing (SA), Genetic algorith m (GA), and Particle swarm optimization (PSO). In addition to that, we will present

Rosario Toscano

362

Convex Graph Invariants  

E-print Network

Dec 2, 2010 ... Massachusetts Institute of Technology. Cambridge, MA 02139 ... best understood using structural properties of graphs. ...... normal cone at x with respect to C, again following the usual conventions in convex analysis [35]: 19 ...

2010-12-02

363

Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems  

PubMed Central

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants. PMID:24723827

Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka

2014-01-01

364

Improved particle swarm optimization with a collective local unimodal search for continuous optimization problems.  

PubMed

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants. PMID:24723827

Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka

2014-01-01

365

Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements  

Microsoft Academic Search

An old dream of computer scientists is to build an optimally efficient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Godel's celebrated self-referential formulas (1931). Our Godel machine's initial software includes an axiomatic description of: the Godel machine's hardware, the problem-specific utility function (such as the expected future reward of

Juergen Schmidhuber

2003-01-01

366

A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem  

E-print Network

A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem Ken Mc Optimization Algorithm for the Chemical and Phase Equilibrium Problem * KEN MCKINNON AND MARCEL MONGEAU ken the problem of finding the number, K, of phases present at equilibrium and their composition, in a chemical

Neumaier, Arnold

367

A fast algorithm for power system optimization problems using an interior point method  

Microsoft Academic Search

An implementation of the dual affine (DA) algorithm, which is a variant of Karmarkar's interior point method, is described. In the DA algorithm, the problem solved is usually the dual of the original linear programming (LP) problem, and it is applicable to linear and nonlinear optimization problems. An application of the proposed optimization technique to hydro-scheduling is presented. The largest

K. Ponnambalam; V. H. Quintana; A. Vannelli

1992-01-01

368

Dynamical systems-based optimal control of incompressible fluids  

Microsoft Academic Search

For optimal control problems related to fluid flow the choice of an adequate cost functional for suppression of vortices is of significant importance. In this research we propose a cost functional based on a local dynamical systems characterization of vortices. The resulting functional is a non-convex function of the velocity gradient tensor. The resulting optimality system describing first order necessary

Michael Hintermüller; Karl Kunisch; Yulian Spasov; Stefan Volkwein

2004-01-01

369

Fabrication-Adaptive Optimization, with an Application to Photonic ...  

E-print Network

In light of the fact that the FA optimization problem (2)-(3) can be non-convex, it makes most practical ..... As (20) is a linear program parameterized by x, it would be convenient to prove Proposition 5 by .... If x? ? x ? ?tol, stop. ...... In the language of robust optimization, the constraints of (49) immunize the inequality “f(

2013-07-20

370

Solving a class of geometric programming problems by an efficient dynamic model  

NASA Astrophysics Data System (ADS)

In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve geometric programming (GP) problems. The main idea is to convert the GP problem into an equivalent convex optimization problem. A neural network model is then constructed for solving the obtained convex programming problem. By 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 optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient.

Nazemi, Alireza; Sharifi, Elahe

2013-03-01

371

Some problems of optimizing shell shape and thickness distribution on the basis of a genetic algorithm  

Microsoft Academic Search

We consider problems related to designing axisymmetric shells of minimal weight (mass) and the development of efficient nonlocal\\u000a optimization methods. The optimization problems under study consist in simultaneous search for the optimal geometry and the\\u000a shell thickness optimal distribution from the minimal weight condition under strength constraints and additional geometric\\u000a constraints imposed on the thickness function, the transverse cross-section radii

N. V. Banichuk; S. Yu. Ivanova; E. V. Makeev

2007-01-01

372

An improved game theory based approach to one type of H-infinity optimal control problems  

Microsoft Academic Search

In this paper we convert H-infinity optimal control problems with linear quadratic objective functions to a regular optimal regulator problem by improving a game theory based approach (Basar and Bernhard, 1991), in which the critical lambdainfin* plays a key role. An alternative and optimal-control-related method of theoretically defining lambdacirc is presented. Instead of solving the H-infinity problem, we solve a

Dan Shen

2006-01-01

373

Advancement and analysis of Gauss pseudospectral transcription for optimal control problems  

E-print Network

As optimal control problems become increasingly complex, innovative numerical methods are needed to solve them. Direct transcription methods, and in particular, methods involving orthogonal collocation have become quite ...

Huntington, Geoffrey Todd, 1979-

2007-01-01

374

Using duality to solve discrete optimization problems: Theory and computational experience  

Microsoft Academic Search

Meaningful dual problems have recently been identified for the integer programming problem, the resource constrained network\\u000a scheduling problem and the traveling salesman problem. In this paper a general class of discrete optimization problem is given\\u000a for which dual problems of this type may be derived. We discuss the use of dual problems for obtaining strong bounds, feasible\\u000a solutions, and for

M. L. Fisher; W. D. Northup; J. F. Shapiro

375

Finite element approximation of an optimal control problem for the von Karman equations  

NASA Technical Reports Server (NTRS)

This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

Hou, L. Steven; Turner, James C.

1994-01-01

376

Inverse Time Dependency in Convex Regularized Learning  

Microsoft Academic Search

In the conventional regularized learning, training time increases as the training set expands. Recent work on L2 linear SVM challenges this common sense by proposing the inverse time dependency on the training set size. In this paper, we first put forward a Primal Gradient Solver (PGS) to effectively solve the convex regularized learning problem. This solver is based on the

Zeyuan Allen Zhu; Weizhu Chen; Chenguang Zhu; Gang Wang; Haixun Wang; Zheng Chen

2009-01-01

377

New approach for the solution of optimal control problems on parallel machines. Doctoral thesis  

SciTech Connect

This thesis develops a highly parallel solution method for nonlinear optimal control problems. Balakrishnan's epsilon method is used in conjunction with the Rayleigh-Ritz method to convert the dynamic optimization of the optimal control problem into a static optimization problem. Walsh functions and orthogonal polynomials are used as basis functions to implement the Rayleigh-Ritz method. The resulting static optimization problem is solved using matrix operations which have well defined massively parallel solution methods. To demonstrate the method, a variety of nonlinear optimal control problems are solved. The nonlinear Raleigh problem with quadratic cost and nonlinear van der Pol problem with quadratic cost and terminal constraints on the states are solved in both serial and parallel on an eight processor Intel Hypercube. The solutions using both Walsh functions and Legendre polynomials as basis functions are given. In addition to these problems which are solved in parallel, a more complex nonlinear minimum time optimal control problem and nonlinear optimal control problem with an inequality constraint on the control are solved. Results show the method converges quickly, even from relatively poor initial guesses for the nominal trajectories.

Stech, D.J.

1990-01-01

378

A Primal-Dual Iterative Scheme for Solving Capacity Planning Problems under Uncertainty  

NASA Astrophysics Data System (ADS)

In this paper we present an application of robust optimization to capacity planning problems under uncertainty. We present the framework to handle uncertainty and discuss the computational complexity of capacity planning problems under this framework. We show that the formulation is not only intuitive but the computational complexity of a large variety of problems is the same as linear (in general convex) programming.

Aswal, Abhilasha; Prasanna, G. N. Srinivasa

2010-10-01

379

A Convex Approach to Fault Tolerant Control  

NASA Technical Reports Server (NTRS)

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.

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

2002-01-01

380

Optimal experimental design applied to DC resistivity problems  

E-print Network

The systematic design of experiments to optimally query physical systems through manipulation of the data acquisition strategy is termed optimal experimental design (OED). This dissertation introduces the state-of-the-art ...

Coles, Darrell Ardon, 1971-

2008-01-01

381

ADAPTIVE PENALTY METHODS FOR GENETIC OPTIMIZATION OF CONSTRAINED COMBINATORIAL PROBLEMS  

E-print Network

. Computers/computer science - Artificial intelligence This research uses the heuristic optimization technique of Genetic Algorithms, which is sometimes considered an artificial intelligence technique. 2. Facilities. Programming - Integer - Heuristic A heuristic optimization technique is used. 4. Reliability - Redundancy

Smith, Alice E.

382

On large scale unconstrained optimization problems and higher ...  

E-print Network

In: Nonlinear Optimization, M. J. D. Powell (Ed.), Academic Press, New York, NY, pp. 301–312. ... Algorithms, Addison-Wesley. [13] Bagirov, A.M. ... [19] Schwefel, H. P., 1981, Numerical Optimization of Computer Models, John Wiley and Sons,.

2008-08-29

383

An accelerated first-order method for solving SOS relaxations of unconstrained polynomial optimization problems  

E-print Network

Our interest lies in solving sum of squares (SOS) relaxations of large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, ...

Bertsimas, Dimitris J.

384

An Exact Algorithm for Optimal Areal Positioning Problem with Rectangular Targets and Requests  

E-print Network

In this thesis, we introduce a new class of problems, which we call Optimal Areal Positioning (OAP), and study a special form of these problems. OAPs have important applications in earth observation satellite management, tele-robotics, multi...

Bansal, Manish

2011-02-22

385

Optimization of evacuation instructions as a fixed-point problem  

E-print Network

phone: +31 15 2785475 fax: +31 15 2783179 s.p.hoogendoorn@tudelft.nl May 2011 Abstract In this paper) people act out of a user- instead of system-optimal thinking. Giving optimized instructions to the people et al. (in press, 2011)), we developed a metaheuristic for the optimization of evacuation guidance

Bierlaire, Michel

386

Structural approaches to spin glasses and optimization problems  

NASA Astrophysics Data System (ADS)

We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by M. Aizenman et al. for non-diluted spin glasses. We use this concept to find generalized bounds for the free energy of the Viana-Bray model of diluted spin glasses and to formulate and prove the Extended Variational Principle that implicitly provides the free energy of the model. Then we exhibit a theorem for the limiting RaMOSt, analogous to the one found by F. Guerra for the Sherrington-Kirkpatrick model, that describes some stability properties of the model. We also show how our technique can be used to prove the existence of the thermodynamic limit of the free energy. We then propose an ultrametric breaking of replica symmetry for diluted spin glasses in the framework of Random Multi-Overlap Structures (RaMOSt). Such a proposal is closer to the Parisi theory for non-diluted spin glasses than the theory based on the iterative approach. Our approach allows to formulate an ansatz in which the Broken Replica Symmetry trial function depends on a set of numbers, over which one has to take the infimum (as opposed to a nested chain of probabilty distributions). Our scheme suggests that the order parameter is determined by the probability distribution of the multi-overlap in a similar sense as in the non-diluted case, and it is not necessarily a functional. Such results are then extended to the K-SAT and p-XOR-SAT optimization problems, and to the spherical mean field spin glass. The ultrametric structure exhibits a factorization property similar to the one of the optimal structures for the Viana-Bray model. The present work paves the way to a revisited Parisi theory for diluted spin systems. Moreover, it emphasizes some structural analogies among different models, which also seem to be plausible for models that still escape good mathematical control. This structural analysis seems quite promising both mathematically and physically.

de Sanctis, Luca

387

Optimal Molecular Design under Property Prediction Uncertainty  

E-print Network

nonlinearstochasticformula- tion into a deterministic MINLP problem with linear binary and convex continuous parts plethora of different potential molecular alternatives. One can already find in the literature success), mixed- integer linear optimization for linear structure-property 1250 May 1997 Vol. 43, No. 5 AICh

Maranas, Costas

388

Nonsmooth optimization-based beamforming in multiuser wireless relay networks  

Microsoft Academic Search

The amplify-and-forward (AF) relay beamforming problems are naturally formulated as indefinite quadratic (nonconvex) optimization programs. The typical methods for solving such optimization problems are to transform them into convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped to obtain solvable SDP relaxed problems and randomization techniques are employed for seeking the feasible

A. H. Phan; H. D. Tuan; H. H. Kha; Ha H. Nguyen

2010-01-01

389

Continuous Blooming of Convex Polyhedra  

E-print Network

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number ...

Demaine, Erik D.

390

On k-convex polygons  

E-print Network

We introduce a notion of k -convexity and explore polygons in the plane that have this property. Polygons which are k -convex can be triangulated with fast yet simple algorithms. However, recognizing them in general is ...

Aichholzer, Oswin

391

Convex Quantum Logic  

E-print Network

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. This differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement.

F. Holik; C. Massri; N. Ciancaglini

2010-08-24

392

A Knowledge-Based Ant Colony Optimization for Flexible Job Shop Scheduling Problems  

Microsoft Academic Search

A Knowledge-Based Ant Colony Optimization (KBACO) algorithm is proposed in this paper for the Flexible Job Shop Scheduling Problem (FJSSP). KBACO algorithm provides an effective integration between Ant Colony Optimization (ACO) model and knowledge model. In the KBACO algorithm, knowledge model learns some available knowledge from the optimization of ACO, and then applies the existing knowledge to guide the current

Li-Ning Xing; Ying-Wu Chen; Peng Wang; Qing-Song Zhao; Jian Xiong

2010-01-01

393

Two?stage profit optimization model for linear scheduling problems considering cash flow  

Microsoft Academic Search

Linear projects with repetitive activity in units are considered for investigation, and a two?stage profit optimization model for linear scheduling problems using constraint programming (CP) is proposed. To maintain work continuity for repetitive activities, interruption time and crew availability are addressed, and the optimization process is presented as follows: (1) optimizing the primary objective (project profit); (2) minimizing total interruption

2009-01-01

394

A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems  

E-print Network

1 A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems Nasser R. Sabar1 of the Honey-bee Mating Optimization Algorithm for solv- ing educational timetabling problems. The honey-bee algorithm is a nature inspired algorithm which sim- ulates the process of real honey-bees mating

Qu, Rong

395

ON THE DYNAMIC PROGRAMMING APPROACH FOR OPTIMAL CONTROL PROBLEMS OF PDE'S WITH AGE STRUCTURE  

Microsoft Academic Search

A survey and some new results are presented concerning the dynamic programming for a class of optimal control problems of partial differential equations with age-structure and of delay systems that include some applied examples from economic theory and from population dynamics. A general optimal control problem in Hilbert spaces applying to all examples is investigated, with particular stress on one

SILVIA FAGGIAN; FAUSTO GOZZI

2004-01-01

396

Learning the Dominance in Diploid Genetic Algorithms for Changing Optimization Problems  

E-print Network

their performance [3], of which using memory schemes is one major approach. The basic principle of memory schemesLearning the Dominance in Diploid Genetic Algorithms for Changing Optimization Problems Shengxiang for genetic al- gorithms to address dynamic optimization problems. This paper proposes an adaptive dominance

Yang, Shengxiang

397

20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev  

E-print Network

20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev ABSTRACT. The appearance of optimization problems in the field of air pollution modeling and their importance arising in air pollution modeling will be considered. We shall present a review of some approaches

Dimov, Ivan

398

Coarse-grained parallel genetic algorithm applied to a nuclear reactor core design optimization problem  

Microsoft Academic Search

This work extends the research related to genetic algorithms (GA) in core design optimization problems, which basic investigations were presented in previous work. Here we explore the use of the Island Genetic Algorithm (IGA), a coarse-grained parallel GA model, comparing its performance to that obtained by the application of a traditional non-parallel GA. The optimization problem consists on adjusting several

Cláudio M. N. A. Pereira; Celso M. F. Lapa

2003-01-01

399

Zero Duality Gap in Optimal Power Flow Problem Javad Lavaei and Steven H. Low  

E-print Network

. This sufficient condition holds for IEEE systems after small resistance (10-5 per unit) is added to every1 Zero Duality Gap in Optimal Power Flow Problem Javad Lavaei and Steven H. Low Abstract--The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose

Low, Steven H.

400

Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems  

Microsoft Academic Search

We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method.

Hans D. Mittelmann

2001-01-01

401

Construction of non-convex polynomial loss functions for training a binary classifier with quantum annealing  

E-print Network

Quantum annealing is a heuristic quantum algorithm which exploits quantum resources to minimize an objective function embedded as the energy levels of a programmable physical system. To take advantage of a potential quantum advantage, one needs to be able to map the problem of interest to the native hardware with reasonably low overhead. Because experimental considerations constrain our objective function to take the form of a low degree PUBO (polynomial unconstrained binary optimization), we employ non-convex loss functions which are polynomial functions of the margin. We show that these loss functions are robust to label noise and provide a clear advantage over convex methods. These loss functions may also be useful for classical approaches as they compile to regularized risk expressions which can be evaluated in constant time with respect to the number of training examples.

Ryan Babbush; Vasil Denchev; Nan Ding; Sergei Isakov; Hartmut Neven

2014-06-17

402

Optimal Conditions for the Control Problem Associated to a Biomedical Process  

NASA Astrophysics Data System (ADS)

This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.

Bund?u, O.; Juratoni, A.; Chevere?an, A.

2010-09-01

403

A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory  

E-print Network

We obtain a version of Noether's invariance theorem for optimal control problems with a finite number of cost functionals. The result is obtained by formulating E. Noether's result to optimal control problems subject to isoperimetric constraints, and then using the unimprovable (Pareto) notion of optimality. A result of this kind was posed to the author, as a mathematical open question, of great interest in applications of control engineering, by A. Gugushvili.

Delfim F. M. Torres

2004-11-08

404

Extremal optimization at the phase transition of the three-coloring problem  

Microsoft Academic Search

We investigate the phase transition in vertex coloring on random graphs, using the extremal optimization heuristic. Three-coloring is among the hardest combinatorial optimization problems and is equivalent to a 3-state anti-ferromagnetic Potts model. Like many other such optimization problems, it has been shown to exhibit a phase transition in its ground state behavior under variation of a system parameter: the

Stefan Boettcher; Allon G. Percus

2004-01-01

405

Convexity Recognition of the Union of Polyhedra  

Microsoft Academic Search

In this paper we consider the following basic problem in polyhedral computation:Given two polyhedra in Rd, P and Q, decide whether their union is convex, and, if so,compute it. We consider the three natural specializations of the problem: (1) when thepolyhedra are given by halfspaces (H-polyhedra) (2) when they are given by verticesand extreme rays (V-polyhedra) (3) when both H-

Alberto Bemporad; Fabio D. Torrisi; Komei Fukuda

2000-01-01

406

Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems.  

SciTech Connect

We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.

Heinkenschloss, Matthias (Rice University, Houston, TX); Bartlett, Roscoe Ainsworth; Van Bloeman Waanders, Paul; Ridzal, Denis (Rice University, Houston, TX)

2005-04-01

407

Error rates of the maximum-likelihood detector for arbitrary constellations: convex\\/concave behavior and applications  

Microsoft Academic Search

Motivated by a recent surge of interest in convex optimization techniques, convexity\\/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex\\/concave for arbitrary multidimensional constellations. In particular, the SER is convex in SNR for

Sergey Loyka; Victoria Kostina; François Gagnon

2010-01-01

408

On interior-point Newton algorithms for discretized optimal control problems with state constraints  

Microsoft Academic Search

In this paper we consider a class of nonlinear programming problems that arise from the discretization of optimal control problems with bounds on both the state and the control variables. For this class of problems, we analyze constraint qualifications and optimality conditions in detail. We derive an affine-scaling and two primal-dual interior-point Newton algorithms by applying, in an interior-point way,

Luis S. Vicente

1998-01-01

409

Computational and statistical tradeoffs via convex relaxation.  

PubMed

Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time or space. Our approach to this problem is to define a notion of "algorithmic weakening," in which a hierarchy of algorithms is ordered by both computational efficiency and statistical efficiency, allowing the growing strength of the data at scale to be traded off against the need for sophisticated processing. We illustrate this approach in the setting of denoising problems, using convex relaxation as the core inferential tool. Hierarchies of convex relaxations have been widely used in theoretical computer science to yield tractable approximation algorithms to many computationally intractable tasks. In the current paper, we show how to endow such hierarchies with a statistical characterization and thereby obtain concrete tradeoffs relating algorithmic runtime to amount of data. PMID:23479655

Chandrasekaran, Venkat; Jordan, Michael I

2013-03-26

410

Optimization Problems in Natural Gas Transportation Systems: A ...  

E-print Network

pipeline systems, namely gathering, transmission, and distribution systems. ... serve as a useful tool to gain insight into the evolution of the many real-life applications ...... The model is solved by means of a particle swarm optimization (

2014-09-15

411

Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling  

PubMed Central

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem. PMID:25243220

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

2014-01-01

412

Singular optimal control and the identically non-regular problem in the calculus of variations  

NASA Technical Reports Server (NTRS)

A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.

Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.

1985-01-01

413

The a posteriori decision in multiobjective optimization problems with smarts, promethee II, and a fuzzy algorithm  

Microsoft Academic Search

In this paper, three decision making methods-Smarts, Promethee, and a fuzzy decision algorithm-were utilized to choose the final optimal solution of multiobjective problems. An inverse electromagnetic scattering problem, as well as some analytical problems, was considered in this study. The a posteriori decision was performed by applying each method to the nondominated front previously met by an evolutionary algorithm. The

Roberta O. Parreiras; João H. R. D. Maciel; João A. Vasconcelos

2006-01-01

414

A global optimization method, ?BB, for general twice-differentiable constrained NLPs—II. Implementation and computational results  

Microsoft Academic Search

Part I of this paper (Adjiman et al., 1998a) described the theoretical foundations of a global optimization algorithm, the ?BB algorithm, which can be used to solve problems belonging to the broad class of twicedifferentiable NPLs. For any such problem, the ability to automatically generate progressively tighter convex lower bounding problems at each iteration guarantees the convergence of the branch-and-bound

C. S. Adjiman; I. P. Androulakis; C. A. Floudas

1998-01-01

415

A Solution to Static Inverse Optimization Problems with Quadratic Constraintsby Learning of Neural Networks  

NASA Astrophysics Data System (ADS)

In this paper we propose a novel approach to static inverse optimization problems with quadratic constraints by learning of neural networks for interpreting real-world data. This proposal has an advantage in that marginal rates of substitution change smoothly in contrast to the case of static inverse optimization with linear constraints. Based on this characteristic, more accurate interpretation of data by static inverse optimization becomes possible. To evaluate the effectiveness of the proposed method, we solve static inverse optimization problems with quadratic constraints using artificial data. We also propose a method to generate quadratic constraints from given data.

Zhang, Hong; Ishikawa, Masumi

416

Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols  

Microsoft Academic Search

A mathematical model for the computation of the phase equilibrium related to atmospheric organic aerosols is presented. The\\u000a phase equilibrium is given by the global minimum of the Gibbs free energy for a system that involves water and organic components.\\u000a This minimization problem is equivalent to the determination of the convex hull of the corresponding molar Gibbs free energy\\u000a function.

N. R. Amundson; A. Caboussat; J. W. He; J. H. Seinfeld

2006-01-01

417

Optimizing material properties of composite plates for sound transmission problem  

NASA Astrophysics Data System (ADS)

To calculate the specific transmission loss (TL) of a composite plate, the conjugate gradient optimization method is utilized to estimate and optimize material properties of the composite plate in this study. For an n-layer composite plate, a nonlinear dynamic stiffness matrix based on the thick plate theory is formulated. To avoid huge computational efforts due to the combination of different composite material plates, a transfer matrix approach is proposed to restrict the dynamic stiffness matrix of the composite plate to a 4×4 matrix. Moreover, the transfer matrix approach has also been used to simplify the complexity of the objective function gradient for the optimization method. Numerical simulations are performed to validate the present algorithm by comparing the TL of the optimal composite plate with that of the original plate. Small number of iterations required during convergence tests illustrates the efficiency of the optimization method. The results indicate that an excellent estimation for the composite plate can be obtained for the desired sound transmission.

Tsai, Yu-Ting; Pawar, S. J.; Huang, Jin H.

2015-01-01

418

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints  

NASA Astrophysics Data System (ADS)

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.

Lim, Byung Hwa; Shin, Yong Hyun; Choi, U. Jin

2008-09-01

419

Initial parameters problem of WNN based on particle swarm optimization  

NASA Astrophysics Data System (ADS)

The stock price prediction by the wavelet neural network is about minimizing RMSE by adjusting the parameters of initial values of network, training data percentage, and the threshold value in order to predict the fluctuation of stock price in two weeks. The objective of this dissertation is to reduce the number of parameters to be adjusted for achieving the minimization of RMSE. There are three kinds of parameters of initial value of network: w , t , and d . The optimization of these three parameters will be conducted by the Particle Swarm Optimization method, and comparison will be made with the performance of original program, proving that RMSE can be even less than the one before the optimization. It has also been shown in this dissertation that there is no need for adjusting training data percentage and threshold value for 68% of the stocks when the training data percentage is set at 10% and the threshold value is set at 0.01.

Yang, Chi-I.; Wang, Kaicheng; Chang, Kueifang

2014-04-01

420

Islanding model for preventing wide-area blackouts and the issue of local solutions of the optimal power flow problem  

E-print Network

Optimization plays a central role in the control and operation of electricity power networks. In this thesis we focus on two very important optimization problems in power systems. The first is the optimal power flow ...

Bukhsh, Waqquas Ahmed

2014-07-01

421

Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations  

E-print Network

This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general ...

Mittal, Shashi, Ph. D. Massachusetts Institute of Technology

2011-01-01

422

Evolutionary Multi-Objective optimization for nurse scheduling problem  

Microsoft Academic Search

Nurse scheduling problem (NSP) is the problem of determining a reasonable and efficient work schedule for nurses. This paper presents a new external memory-based approach along with Multi-Objective Genetic Algorithms (MOGA) to solve multiobjective NSPs. In multiobjective modeling of NSPs, there are several objectives which are in conflict with each other, and there are some hard constraints that should be

Omid Sharif; Ahmet Ünveren; Adnan Acan

2009-01-01

423

Boundedness of optimal matrices in extremal multigraph and digraph problems  

Microsoft Academic Search

We consider multigraphs in which any two vertices are joined by at mostq edges, and study the Turán-type problem for a given family of forbidden multigraphs. In the caseq=2, answering a question of Brown, Erdos and Simonovits, we obtain an explicit upper bound on the size of the matrix generating an asymptotical solution of the problem. In the caseq>2 we

Alexander Sidorenko

1993-01-01

424

Algebraic Optimization: The Fermat-Weber Location Problem  

Microsoft Academic Search

The Fermat-Weber location problem is to find a point in Rn that minimizes the sum of the (weighted) Euclidean distances fromm given points in Rn. In this work we discuss some relevant complexity and algorithmic issues. First, using Tarski's theory on solvability over real closed fields we argue that there is an infinite scheme to solve the problem, where the

R. Chandrasekaran; Arie Tamir

1990-01-01

425

A New Method for Mapping Optimization Problems onto Neural Networks  

E-print Network

is presented. We consider the graph partition and the travelling salesman problems. The key new ingredient as time consumption goes even when executed serially. When generalizing to graph partition (GP) the N exploratory numerical studies on modest­sized samples. In ref. [2] the graph bisection problem was mapped onto

Peterson, Carsten

426

Real-Time Mass Passenger Transport Network Optimization Problems  

Microsoft Academic Search

The aim of the real-time mass transport vehicle routing problem (MTVRP) is to find a solution to route n vehicles in real time to pick up and deliver m passengers. This problem is described in the context of flexible large-scale mass transportation options that use new technologies for communication among passengers and vehicles. This study does not focus on the

Laia Pages; R. Jayakrishnan

2006-01-01

427

On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems  

Microsoft Academic Search

Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density $f$ of a random variable $X$ based on $n$ i.i.d. observations from $Y = X + \\\\varepsilon$, where $\\\\varepsilon$ is a measurement error with a known distribution. In this paper, the effect of errors in variables of nonparametric deconvolution is examined. Insights

Jianqing Fan

1991-01-01

428

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

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

429

Solution of transient optimization problems by using an algorithm based on nonlinear programming  

NASA Technical Reports Server (NTRS)

An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.

Teren, F.

1977-01-01

430

A primal-dual potential reduction method for problems involving matrix inequalities  

Microsoft Academic Search

We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and gener- alizes Gonzaga and Todd's method for linear programming. A worst-case analysis shows that the number of iterations grows as the square root of the problem size, but in practice it appears to grow

Lieven Vandenberghe; Stephen P. Boyd

1995-01-01

431

Parallel evolutionary algorithms for optimization problems in aerospace engineering  

Microsoft Academic Search

This paper presents the recent developments in hierarchical genetic algorithms (HGAs) to speed up the optimization of aerodynamic shapes. It first introduces HGAs, a particular instance of parallel GAs based on the notion of interconnected sub-populations evolving independently. Previous studies have shown the advantages of introducing a multi-layered hierarchical topology in parallel GAs. Such a topology allows the use of

J. F. Wang; J. Periaux; M. Sefrioui

2002-01-01

432

Self-Organizing Multiagent Approach to Optimization in Positioning Problems  

E-print Network

is to minimize the weighted distance between the demand points and the facilities. The proposed model relies, this is not at all surprising since location policy is one of the most profitable areas of applied systems analysis, hospitals, fire stations, etc. The general prob- lem is, then, the location of new facilities to optimize

Simonin, Olivier -Département Informatique, Institut National des Sciences Appliquées de Lyon

433

Genetic Algorithms for Combinatorial Optimization: The Assembly Line Balancing Problem  

E-print Network

have looked at the application of genetic algorithms to optimization of nonlinear functions; our algorithm works. The method operates with a set of potential solutions. This is referred to as a population individuals. Based on this fitness function a number of individuals are selected as potential parents

Ferris, Michael C.

434

A "HUM" conjugate gradient algorithm for constrained nonlinear optimal control : terminal and regular problems  

E-print Network

Optimal control problems often arise in engineering applications when a known desired behavior is to be imposed on a dynamical system. Typically, there is a performance and controller use trade-off that can be quantified ...

Oliveira, Ivan B. (Ivan Borges), 1975-

2002-01-01

435

Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem  

PubMed Central

Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem. PMID:23935429

Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi

2013-01-01

436

Two-Stage Robust Power Grid Optimization Problem  

E-print Network

A utility company solves the traditional unit commitment problem plus transmission capacity .... objective value or facilitate the scheduling of other generation units. ...... In this sense, the WC gaps measure the relative infeasibility of the nominal ...

2011-01-02

437

Optimization technique for problems with an inequality constraint  

NASA Technical Reports Server (NTRS)

General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.

Russell, K. J.

1972-01-01

438

Improved Bounds for the Traveling Umpire Problem - Optimization ...  

E-print Network

Aug 28, 2013 ... (Wright, 1991), football (Yavuz et al., 2008), and tennis (Farmer et al., 2007). .... Table 1: Number of best-known solutions found by existing solution methods according ...... ball umpires and the traveling umpire problem.

2013-08-28

439

New high performing hybrid particle swarm optimization for permutation flow shop scheduling problem with minimization of makespan  

Microsoft Academic Search

The well-known particle swarm optimization (PSO) proposed by Kennedy and Eberhart has been widely applied to the continuous optimal problems. However, it is still intractable to apply PSO to discrete optimization problems, such as permutation flow shop scheduling problems (PFSSP). In this paper, a new high performing metaheuristic algorithm hybridizing PSO with variable neighborhood search (VNS) is proposed to solve

Y. Sun; M. Liu; C. Y. Zhang; L. Gao; K. L. Lian

2010-01-01

440

Some optimal control problems for a two-phase field model of solidification  

Microsoft Academic Search

In this paper we deal with some optimal control problems for a solidification phase field model of metallic alloys. The model\\u000a allows crystallizations of two kinds, each one described by its own phase field. Accordingly, the state is the triplet (?,u,v), where ? is the temperature and u and v are phase field functions. The optimality conditions for the optimal

José Luiz Boldrini; Bianca Morelli Calsavara Caretta; Enrique Fernández-Cara

2010-01-01

441

An algorithm for solving optimal control problems with control and terminal-state constraints  

Microsoft Academic Search

The authors (1993) introduced an algorithm to solve continuous-time optimal control problems where the control variables are constrained. In this paper, the algorithm is extended to solve optimal control problems with not only hard control constraints but also terminal-state constraints. An exact penalty type of function is employed to penalize any violated terminal-state constraints. The authors then show that the

Baoming Ma; William S. Levine

1994-01-01

442

Application of separable programming to the optimization of a water resource system problem  

E-print Network

APPLICATION OF SEPARABLE PROGIVQBiING TO THE OPTIMIZATION OF A MATER RESOURCE SYSTEM PROBLEM A Thesis JACK ROBERT MAGNESS Submitted to the Graduate College of Texas A&M University in partial fulfillment of the requirement for the degr...'ee of MASTER OF SCIENCE December 1974 Major Subject: Mathematics APPLICATION OF SEPARABLE PROGRAMMING TO THE OPTIMIZATION OF A WATER RESOURCE SYSTEM PROBLEM A Thesis by JACK ROBERT MAGNESS Approved as to style and content by: op (Chairman of ittee...

Magness, Jack Robert

1974-01-01

443

Evaluating significant economic trade-offs for process design and steady-state control optimization problems  

Microsoft Academic Search

An order-of-magnitude analysis that evaluates the significant economic trade-offs for the process design optimization problem allows rapid screening of flowsheet alternatives. The optimization problem is simplified by eliminating all but the most important design variables and by including only the dominant cost functions for each trade-off. Quantitative parameters are defined which allow a straightforward selection of these elements and identify

W. R. Fisher; M. F. Doherty; J. M. Douglas

1985-01-01

444

UFO: Uncertainty Feature Optimization, an Implicit Paradigm for Problems with Noisy Data  

Microsoft Academic Search

Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the general

Niklaus Eggenberg; Matteo Salani; Michel Bierlaire

2008-01-01

445

On the Dynamical Programming Equation of Risk Sensitive Control Problem Associated to an Optimal Investment Model  

Microsoft Academic Search

The study in Fleming(F1) brings a connection of some optimal investment problem and the theory of risk sensitive control. From this, the method of dynamical programming can be used. Then the dynamical programming equation can be derived. It is a nonlinear partial differential equation. A solution gives a candidate of optimal portfolio. We consider a particular investment model( is refered

H. Kaise; S. J. Sheu

446

An Optimal Solution to a General Dynamic Jet Fuel Hedging Problem  

E-print Network

combine dynamic programming and Kalman filter estimation to obtain an optimal policy that minimizesAn Optimal Solution to a General Dynamic Jet Fuel Hedging Problem Juliana M. Nascimento Warren B #12;Abstract We propose a dynamic hedging strategy for jet fuel which strikes a balance between

Powell, Warren B.

447

Biogeography-Based Optimization and the Solution of the Power Flow Problem  

E-print Network

Biogeography-Based Optimization and the Solution of the Power Flow Problem Rick Rarick, Dan Simon and emigration between the islands. This paper presents an application of the BBO algorithm to the power flow algorithm consistently performs better than the GA in determining an optimal solution to the power flow

Simon, Dan

448

Tracking and Optimal Control Problems in Human Head/Eye Coordination  

E-print Network

-- Head Movement, Eye Movement, Listing's Law, Donders' Surface, Vestibulo-ocular reflex, Optimal ConTracking and Optimal Control Problems in Human Head/Eye Coordination Indika Wijayasinghe1, Eugenio Aulisa1, Bijoy K. Ghosh1, Stefan Glasauer2,3 and Olympia Kremmyda4 Abstract-- Human head and eye rotate

Ghosh, Bijoy K.

449

A shooting method for the numerical solution of optimal periodic control problems  

Microsoft Academic Search

A shooting type numerical optimization technique is developed by taking into account the particular characteristics of the periodic optimal control problem. The algorithm first closes a starting trajectory to one that satisfies all of the first order necessary conditions except the transversality condition associated with free period. Then a one-dimensional family is traced in the direction of improved cost criterion.

Jason L. Speyer; Richard T. Evans

1981-01-01

450

A Level Set Method for Multiobjective Combinatorial Optimization: Application to the Quadratic Assignment Problem  

Microsoft Academic Search

Multiobjective combinatorial optimization problems have received increasing attention in recent years. Nevertheless, many algorithms are still restricted to the bicriteria case. In this paper we propose a new algorithm for computing all Pareto optimal solutions. Our algorithm is based on the notion of level sets and level curves and contains as a subproblem the determination of K best solutions for

Matthias Ehrgott; Thomas Stephan; Dagmar Tenfelde-Podehl

2002-01-01

451

An optimal birth control problem for a dynamical population model with size-structure  

Microsoft Academic Search

This work is concerned with an optimal control problem for a size-structured population model, which takes fertility as the control variable. Existence and uniqueness of solutions to the basic state system and the dual system are proven via the Banach fixed point theorem. Necessary optimality conditions of first order are established in the form of an Euler-Lagrange system by the

Ze-Rong He; Yan Liu

452

The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots  

E-print Network

The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots of Minnesota Minneapolis, MN 55455 Email: {hjmin|npapas}@cs.umn.edu Abstract-- This work presents a novel multi-robot coverage scheme for an unknown number of robots; it focuses on optimizing the number of robots and each

Minnesota, University of

453

Coupling Simulation and Optimization to Solve Planning Problems in a Fast-Developing Area  

Microsoft Academic Search

In geographical analysis, spatial simulation and optimization are usually separate processes tackling different problems. It is, however, increasingly necessary to integrate them. Particularly in a fast developing area, the development to be simulated is seldom inertial (i.e., strictly following the historical trend); instead, it is likely to be interfered by new planning measures. Meanwhile, in such an area an optimization

Xia Li; Xun Shi; Jinqiang He; Xaioping Liu

2011-01-01

454

A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD FOR AN OPTIMAL DESIGN PROBLEM  

E-print Network

A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD FOR AN OPTIMAL DESIGN PROBLEM S¨OREN BARTELS adaptive finite element method (AFEM). 1. Introduction The optimal design of two materials with given an adaptive algorithm and to analyse it in the spirit of [3, 4, 15, 21, 22, 25]. This adaptive finite element

Bartels, Soeren

455

ANTI-ANGIOGENIC THERAPY IN CANCER TREATMENT AS AN OPTIMAL CONTROL PROBLEM  

E-print Network

ANTI-ANGIOGENIC THERAPY IN CANCER TREATMENT AS AN OPTIMAL CONTROL PROBLEM URSZULA LEDZEWICZ AND HEINZ SCH¨ATTLER Abstract. Anti-angiogenic therapy is a novel treatment approach in cancer therapy. Key words. optimal control, geometric methods, cancer treatment, anti-angiogenic therapy AMS subject

Schaettler, Heinz

456

An FPTAS for Optimizing a Class of Low-Rank Functions Over a ...  

E-print Network

Sep 7, 2011 ... returns a solution which is an extreme point of the polytope. ... Recent work on optimization problems of this kind has focused on the special case when g is quasi-concave (see .... articles for solving multiplicative programming problems can be ...... Interior Point Polynomial Methods in Convex Programming.

457

Localization for Solving Noisy Multi-Objective Optimization Problems  

Microsoft Academic Search

This paper investigates the use of local models in the context of noisy evolutionary multi-objective optimization. Within this technique, the search space is explicitly divided into several non-overlapping hyper-spheres. The mechanism allows evolution and the process of filtering noise within the local spaces of these hyper-spheres, instead of the global space. A direction of improvement, that is related to the

Lam Thu Bui; Hussein A. Abbass; Daryl Essam

2009-01-01

458

Analysis and formulation of a class of complex dynamic optimization problems  

NASA Astrophysics Data System (ADS)

The Direct Transcription approach, also known as the direct simultaneous approach, is a widely used solution strategy for the solution of dynamic optimization problems involving differential-algebraic equations (DAEs). Direct transcription refers to the procedure of approximating the infinite dimensional problem by a finite dimensional one, which is then solved using a nonlinear programming (NLP) solver tailored to large-scale problems. Systems governed by partial differential equations (PDEs) can also be handled by spatially discretizing the PDEs to convert them to a system of DAEs. The objective of this thesis is firstly to ensure that direct transcription using Radau collocation is provably correct, and secondly to widen the applicability of the direct simultaneous approach to a larger class of dynamic optimization and optimal control problems (OCPs). This thesis aims at addressing these issues using rigorous theoretical tools and/or characteristic examples, and at the same time use the results for solving large-scale industrial applications to realize the benefits. The first part of this work deals with the analysis of convergence rates for direct transcription of unconstrained and final-time equality constrained optimal control problems. The problems are discretized using collocation at Radau points. Convergence is analyzed from an NLP/matrix-algebra perspective, which enables the prediction of the conditioning of the direct transcription NLP as the mesh size becomes finer. Several convergence results are presented along with tests on numerous example problems. These convergence results lead to an adjoint estimation procedure given the Lagrange multipliers for the large-scale NLP. The work also reveals the role of process control concepts such as controllability on the convergence analysis, and provides a very important link between control and optimization inside the framework of dynamic optimization. As an effort to extend the applicability of the direct simultaneous approach to a wider class of problems, a PDE-constrained optimal control problem, the spatial discretization of which results in a DAE-constrained problem with an arbitrarily high-index inequality constraint, is studied. Optimal control problems with high-index path constraints are very hard to solve, numerically. Contrary to the intuitive belief that the direct transcription approach would not work for the high-index optimal control problem, an analysis is performed to show that NLP-based methods have flexibility with respect to constraint qualifications, and this can be put to use in the context of high-index inequality path-constrained problems to obtain meaningful solutions. (Abstract shortened by UMI.)

Kameswaran, Shivakumar

459

Multigrid one shot methods for optimal control problems: Infinite dimensional control  

NASA Technical Reports Server (NTRS)

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Arian, Eyal; Taasan, Shlomo

1994-01-01

460

A fast algorithm for power system optimization problems using an interior point method  

SciTech Connect

Linear Programming (LP) is a widely used tool for solving many linear/non-linear power-system optimization problems. Variants of simplex-based methodologies are generally used to solve the underlying LP problems. In this paper an implementation of the newly developed Dual Affine (DA) algorithm (a variant of Karmarkar's interior point method) is described in detail and some computational results are presented. This algorithm is particularly suitable for problems with a large number of constraints, and is applicable to linear and nonlinear optimization problems. An application of the proposed optimization technique to hydro-scheduling is presented; the largest problem is comprised of 880 variable and 3680 constraints, and is solved over 9 times faster than an efficient simplex (MINOS) code.

Ponnambalam, K. (Waterloo Univ., ON (Canada). Dept. of Systems Design Engineering); Quintana, V.H.; Vannelli, A. (Dept. of Electrical and Computer Engineering, Univ., of Waterloo, Waterloo, Ontario N2L 3G1 (CA))

1992-05-01

461

Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization  

NASA Technical Reports Server (NTRS)

A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

462

Optimization of Production Planning Problems - A Case Study for Assembly Lines  

NASA Astrophysics Data System (ADS)

For a few years, Simulated Annealing (SA)1 and related Monte Carlo optimization algorithms like Threshold Accepting (TA)2 have become a useful means for optimizing various kinds of economic problems, like the Traveling Salesman Problem (TSP). In this paper, we concentrate on the production processes themselves because most costs are thereby incurred, such that a small relative improvement can lead to large savings. We will present an application of these physical optimization algorithms for a certain type of assembly lines which can be transferred to a TSP with additional constraints.

Schneider, Johannes; Britze, Jürgen; Ebersbach, Anja; Morgenstern, Ingo; Puchta, Markus

463

Ant Colony Optimization with Memory and Its Application to Traveling Salesman Problem  

NASA Astrophysics Data System (ADS)

Ant Colony Optimization (ACO) is one of the most recent techniques for solving combinatorial optimization problems, and has been unexpectedly successful. Therefore, many improvements have been proposed to improve the performance of the ACO algorithm. In this paper an ant colony optimization with memory is proposed, which is applied to the classical traveling salesman problem (TSP). In the proposed algorithm, each ant searches the solution not only according to the pheromone and heuristic information but also based on the memory which is from the solution of the last iteration. A large number of simulation runs are performed, and simulation results illustrate that the proposed algorithm performs better than the compared algorithms.

Wang, Rong-Long; Zhao, Li-Qing; Zhou, Xiao-Fan

464

The test suite generation problem: Optimal instances and their implications  

Microsoft Academic Search

In the test suite generation problem (TSG) for software systems, I is a set of n input parameters where each I 2 I has (I) data values, and O is a collection of subsets ofI where the interactions of the parameters in each O 2O are thought to aect the outcome of the system. A test case for (I;O; )

Christine T. Cheng

2007-01-01

465

Promoting optimal development: screening for behavioral and emotional problems.  

PubMed

By current estimates, at any given time, approximately 11% to 20% of children in the United States have a behavioral or emotional disorder, as defined in the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition. Between 37% and 39% of children will have a behavioral or emotional disorder diagnosed by 16 years of age, regardless of geographic location in the United States. Behavioral and emotional problems and concerns in children and adolescents are not being reliably identified or treated in the US health system. This clinical report focuses on the need to increase behavioral screening and offers potential changes in practice and the health system, as well as the research needed to accomplish this. This report also (1) reviews the prevalence of behavioral and emotional disorders, (2) describes factors affecting the emergence of behavioral and emotional problems, (3) articulates the current state of detection of these problems in pediatric primary care, (4) describes barriers to screening and means to overcome those barriers, and (5) discusses potential changes at a practice and systems level that are needed to facilitate successful behavioral and emotional screening. Highlighted and discussed are the many factors at the level of the pediatric practice, health system, and society contributing to these behavioral and emotional problems. PMID:25624375

Weitzman, Carol; Wegner, Lynn

2015-02-01

466

Location Problems Optimization by a Self-Organizing Multiagent Approach  

E-print Network

on reactive multiagent systems. The proposed model relies on a set of agents situated in a common envi-organization. Then, we present how the model can be extended to the multi-level version of the location problem. Fi since location policy is one of the most profitable areas of applied systems analysis. This is due

Simonin, Olivier -Département Informatique, Institut National des Sciences Appliquées de Lyon

467

Solving the Prize-Collecting Steiner Tree Problem to Optimality  

Microsoft Academic Search

The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg. fiber optics or district heating) where profit

Ivana Ljubic; René Weiskircher; Ulrich Pferschy; Gunnar W. Klau; Petra Mutzel; Matteo Fischetti

2005-01-01

468

An Asymptotic Method to a Financial Optimization Problem  

NASA Astrophysics Data System (ADS)

This paper studies the borrower’s optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner’s point of view.

Xie, Dejun; Edwards, David; Schleiniger, Giberto

469

An Asymptotic Method to a Financial Optimization Problem  

NASA Astrophysics Data System (ADS)

This paper studies the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner's point of view.

Xie, Dejun; Edwards, David; Schleiniger, Giberto

470

Generalized monotonically convergent algorithms for solving quantum optimal control problems  

NASA Astrophysics Data System (ADS)

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.

Ohtsuki, Yukiyoshi; Turinici, Gabriel; Rabitz, Herschel

2004-03-01

471

Generalized monotonically convergent algorithms for solving quantum optimal control problems.  

PubMed

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior. PMID:15267426

Ohtsuki, Yukiyoshi; Turinici, Gabriel; Rabitz, Herschel

2004-03-22

472

New numerical methods for open-loop and feedback solutions to dynamic optimization problems  

NASA Astrophysics Data System (ADS)

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

Ghosh, Pradipto

473

An Ant Colony Optimization Algorithm for the 2D HP Protein Folding Problem  

E-print Network

An Ant Colony Optimization Algorithm for the 2D HP Protein Folding Problem Alena Shmygelska, Rosal, the two dimensional hydrophobic-polar (2D HP) protein folding problem. We introduce an ant colony algorithm closely approaches that of specialised, state-of-the methods for 2D HP protein folding. 1

Hoos, Holger H.

474

On Variant Strategies To Solve The Magnitude Least Squares Optimization Problem In Parallel  

E-print Network

1 On Variant Strategies To Solve The Magnitude Least Squares Optimization Problem In Parallel to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem), interior point (I-P) methods, semi-definite programming (SDP) and magnitude squared least squares (MSLS

475

Optimization by phases for the flexible job-shop scheduling problem  

Microsoft Academic Search

In this paper, we deal with the flexible job shop scheduling problem. The suggested method is based on an optimization by phases. The first phase is ensured by an assignment technique based on a heuristic approach and local search. The second phase consists in applying a genetic algorithm to deal with the sequencing problem. The approach performance is evaluated by

N. Zribi; I. Kacem; A. El Kamel; P. Borne

2004-01-01

476

A Global Optimization Algorithm for Solving the Minimum Multiple Ratio Spanning Tree Problem  

E-print Network

A Global Optimization Algorithm for Solving the Minimum Multiple Ratio Spanning Tree Problem-of-ratios version of the classical minimum spanning tree (MST) problem. We develop a branch-and-bound algorithm: fractional programming, sum-of-ratios, multiple-ratio minimum spanning tree 1. Introduction A fractional

Butenko, Sergiy

477

Stability of linear vector optimization problems corresponding to an efficient set  

Microsoft Academic Search

This paper deals with the set of all parameters corresponding to the set of all efficient points of parametric linear multiobjective programming problems. Here, we consider two classes of parametric optimization problems one of them is parameters in the objective functions and the other is parameters in the right-hand side of the constraints. An algorithm for determining this set is

Abou-Zaid H. El-Banna; Sana’a A. Zarea

2001-01-01

478

Global optimization for the phase and chemical equilibrium problem: Application to the NRTL equation  

Microsoft Academic Search

Several approaches have been proposed for the computation of solutions to the phase and chemical equilibrium problem when the problem is posed as the minimization of the Gibbs free energy function. None of them can guarantee convergence to the true optimal solution, and are highly dependent on the supplied initial point. Convergence to local solutions often occurs, yielding incorrect phase

C. M. McDonald; C. A. Floudas

1995-01-01

479

Simultaneous optimization of multi-response problems in the Taguchi method using genetic algorithm  

Microsoft Academic Search

The optimization of multiple responses (or performance characteristics) has received increasing attention over the last few years in many manufacturing organizations. Most previous applications of the Taguchi method only emphasize the single-response problems, while the multi-response problems have received relatively little attention. Many Taguchi practitioners have employed past experience and engineering knowledge or judgement when dealing with multiple responses. The

R. Jeyapaul; P. Shahabudeen; K. Krishnaiah

2006-01-01

480

Fast solution of optimal control problems in the selective cooling of steel  

E-print Network

Fast solution of optimal control problems in the selective cooling of steel F. Tr¨oltzsch and A of cooling milled steel profiles at a maximum rate subject to given bounds on the difference of temperatures in prescribed points of the steel profile. This leads to a nonlinear parabolic control problem with state

Chemnitz, Technische Universität

481

Designs Mutually unbiased bases 2-designs from bases Open problems Optimal complex projective designs  

E-print Network

Designs Mutually unbiased bases 2-designs from bases Open problems Optimal complex projective designs Aidan Roy November 6, 2009 #12;Designs Mutually unbiased bases 2-designs from bases Open problems , with equality if and only if X is a t-design. #12;Designs Mutually unbiased bases 2-designs from bases Open

Cameron, Peter

482

Evolutional Solutions by Using PSO for 0-1 Combinatorial Optimization Problems with Constraints  

NASA Astrophysics Data System (ADS)

In this paper, as one of global optimization methods for 0-1 combinatorial optimization problems with constraints, a continuous relaxation approach is presented, in which the continuous variables are transformed into binary variables through a sorting procedure of continuous variables taking the constraints into consideration. The new type of relaxation approach enables us to apply Particle Swarm Optimization, which is effective heuristic method for global optimization with continuous variables. Here, our presented approach is interpreted as one of evolutional computing methods because the transformation of continuous variables into binary ones corresponds to transform genotype into phenotype, which is reverse to a relation in usual evolutional computing.

Ogawa, Naoaki; Aiyoshi, Eitaro

483

Lagrangian support vector regression via unconstrained convex minimization.  

PubMed

In this paper, a simple reformulation of the Lagrangian dual of the 2-norm support vector regression (SVR) is proposed as an unconstrained minimization problem. This formulation has the advantage that its objective function is strongly convex and further having only m variables, where m is the number of input data points. The proposed unconstrained Lagrangian SVR (ULSVR) is solvable by computing the zeros of its gradient. However, since its objective function contains the non-smooth 'plus' function, two approaches are followed to solve the proposed optimization problem: (i) by introducing a smooth approximation, generate a slightly modified unconstrained minimization problem and solve it; (ii) solve the problem directly by applying generalized derivative. Computational results obtained on a number of synthetic and real-world benchmark datasets showing similar generalization performance with much faster learning speed in accordance with the conventional SVR and training time very close to least squares SVR clearly indicate the superiority of ULSVR solved by smooth and generalized derivative approaches. PMID:24374970

Balasundaram, S; Gupta, Deepak; Kapil

2014-03-01

484

Local Search for String Problems: Brute Force is Essentially Optimal  

E-print Network

]. There is substantial work in parameterized local search. For example, con- cerning the Traveling Salesman problem to ask whether nO(k) time is required for searching this neighborhood, or whether f(k) · poly(n) time can to the old one in 4k ·poly(n) time. Marx [13] proved the non-existence of such an algorithm for the edge

Wichmann, Felix

485

Solving the unconstrained optimization problem by a variable neighborhood search  

NASA Astrophysics Data System (ADS)

This paper presents variable neighborhood search (VNS) for the problem of finding the global minimum of a nonconvex function. The variable neighborhood search, which changes systematically neighborhood structures in the search for finding a better solution, is used to guide a set of standard improvement heuristics. This algorithm was tested on some standard test functions, and successful results were obtained. Its performance was compared with the other algorithms, and observed to be better.

Toksari, M. Duran; Guner, Ertan

2007-04-01

486

A numerical study of hybrid optimization methods for the molecular conformation problems  

SciTech Connect

An important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules depends on the accurate determination of their three-dimensional structure or conformation. Under the assumption that molecules will settle into a configuration for which their energy is at a minimum, this design problem can be formulated as a global optimization problem. The solution of the molecular conformation problem can then be obtained, at least in principle, through any number of optimization algorithms. Unfortunately, it can easily be shown that there exist a large number of local minima for most molecules which makes this an extremely difficult problem for any standard optimization method. In this study, we present results for various optimization algorithms applied to a molecular conformation problem. We include results for genetic algorithms, simulated annealing, direct search methods, and several gradient methods. The major result of this study is that none of these standard methods can be used in isolation to efficiently generate minimum energy configurations. We propose instead several hybrid methods that combine properties of several local optimization algorithms. These hybrid methods have yielded better results on representative test problems than single methods.

Meza, J.C.; Martinez, M.L.

1993-05-01

487

The Automatic Formulating Method of the Optimal Operating Planning Problem for Energy Supply Systems  

NASA Astrophysics Data System (ADS)

The problem of the optimal operating planning for energy supply system is formulated as mixed-integer linear programming (MILP), but, it is too complicated for most untrained operators with little experience to apply the method. This paper proposes an automatic evaluating method of the optimal operating planning for energy supply system in using simple data. The problem can be formulated only from characteristics of equipment, tariff of input energy, and energy demands. The connection of equipment is defined as a matrix, and generated from property data of equipment. The constraints and objective function of the problem are generated from relation-ship data in the matrix and characteristics of equipment. An optimization calculation for the problem is automatically carried out. It is confirmed that any operator can evaluate many alternative configurations of the energy supply systems.

Suzuki, Naohiko; Ueda, Takaharu; Sasakawa, Koichi

488

Finding optimal measurements with inconclusive results using the problem of minimum error discrimination  

NASA Astrophysics Data System (ADS)

We propose an approach for finding an optimal measurement for quantum state discrimination that maximizes the probability of correct detection with a fixed rate of inconclusive results. In our approach, we obtain the optimal measurement by solving the problem of finding a measurement that maximizes the weighted sum of the probability of correct detection and that of inconclusive results. We show that this problem can be reduced to the widely studied problem of finding a minimum error measurement for a certain state set, which maximizes the probability of correct detection without inconclusive results. As an application of our approach, we show how to solve the problem of finding an optimal measurement for qubit states with a fixed rate of inconclusive results.

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

2015-02-01

489

A Transformation Approach to Optimal Control Problems with Bounded State Variables  

NASA Technical Reports Server (NTRS)

A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

Hanafy, Lawrence Hanafy

1971-01-01

490

A Dynamic Programming Framework for Combinatorial Optimization Problems on Graphs with Bounded Pathwidth  

E-print Network

In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The problems are relevant for assessing network reliability and improving the network's performance and fault tolerance. The main technique considered in this paper is dynamic programming.

Andreica, Mugurel Ionut

2008-01-01

491

A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems  

Microsoft Academic Search

Many-objective optimization refers to the optimiza- tion problems containing large number of objectives, typically more than four. Non-dominance is an inadequate strategy for convergence to the Pareto front for such problems, as almost all solutions in the population become non-dominated, resulting in loss of convergence pressure. However, for some problems, it may be possible to generate the Pareto front using

Hemant Kumar Singh; Amitay Isaacs; Tapabrata Ray

2011-01-01

492

Finite element solution of optimal control problems with state-control inequality constraints  

NASA Technical Reports Server (NTRS)

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

Bless, Robert R.; Hodges, Dewey H.

1992-01-01

493

Hybrid solution of stochastic optimal control problems using Gauss pseudospectral method and generalized polynomial chaos algorithms  

NASA Astrophysics Data System (ADS)

A hybrid numerical algorithm combining the Gauss Pseudospectral Method (GPM) with a Generalized Polynomial Chaos (gPC) method to solve nonlinear stochastic optimal control problems with constraint uncertainties is presented. TheGPM and gPC have been shown to be spectrally accurate numerical methods for solving deterministic optimal control problems and stochastic differential equations, respectively. The gPC uses collocation nodes to sample the random space, which are then inserted into the differential equations and solved by applying standard differential equation methods. The resulting set of deterministic solutions is used to characterize the distribution of the solution by constructing a polynomial representation of the output as a function of uncertain parameters. Optimal control problems are especially challenging to solve since they often include path constraints, bounded controls, boundary conditions, and require solutions that minimize a cost functional. Adding random parameters can make these problems even more challenging. The hybrid algorithm presented in this dissertation is the first time the GPM and gPC algorithms have been combined to solve optimal control problems with random parameters. Using the GPM in the gPC construct provides minimum cost deterministic solutions used in stochastic computations that meet path, control, and boundary constraints, thus extending current gPC methods to be applicable to stochastic optimal control problems. The hybrid GPM-gPC algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a trajectory optimization problem simulating an aircraft flying through a threat field where exact locations of the threats are unknown. The results show that the expected value, variance, and covariance statistics of the polynomial output function approximations of the state, control, cost, and terminal time variables agree with Monte-Carlo simulation results while requiring on the order of (1/40)th to (1/100)th the number of collocation points and computation time. It was shown that the hybrid algorithm demonstrated an ability to effectively characterize how the solutions to optimization problems vary with uncertainty, and has the potential with continued development and availability of more powerful computer workstations, to be a powerful tool applicable to more complex control problems of interest to the Department of Defense.

Cottrill, Gerald C.

494

Incorporating technology-based learning tools into teaching and learning of optimization problems  

NASA Astrophysics Data System (ADS)

The traditional approach of teaching optimization problems in calculus emphasizes more on teaching the students using analytical approach through a series of procedural steps. However, optimization normally involves problem solving in real life problems and most students fail to translate the problems into mathematic models and have difficulties to visualize the concept underlying. As an educator, it is essential to embed technology in suitable content areas to engage students in construction of meaningful learning by creating a technology-based learning environment. This paper presents the applications of technology-based learning tool in designing optimization learning activities with illustrative examples, as well as to address the challenges in the implementation of using technology in teaching and learning optimization. The suggestion activities in this paper allow flexibility for educator to modify their teaching strategy and apply technology to accommodate different level of studies for the topic of optimization. Hence, this provides great potential for a wide range of learners to enhance their understanding of the concept of optimization.

Yang, Irene

2014-07-01

495

Frustrated systems: Ground state properties via combinatorial optimization  

Microsoft Academic Search

An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered\\u000a systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising model, the\\u000a diluted antiferromagnet in an external field, the spin glass problem, the solid-on-solid model with a disordered substrte\\u000a and other convex cost flow problems occurring

Heiko Rieger

1998-01-01

496

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming  

NASA Technical Reports Server (NTRS)

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

497

A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem  

Microsoft Academic Search

The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region

Jesús M. Jorge

2005-01-01

498

Direct SQP-methods for solving optimal control problems with delays  

SciTech Connect

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

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

1994-12-31

499

Probability-based least square support vector regression metamodeling technique for crashworthiness optimization problems  

NASA Astrophysics Data System (ADS)

This paper presents a crashworthiness design optimization method based on a metamodeling technique. The crashworthiness optimization is a highly nonlinear and large scale problem, which is composed various nonlinearities, such as geometry, material and contact and needs a large number expensive evaluations. In order to obtain a robust approximation efficiently, a probability-based least square support vector regression is suggested to construct metamodels by considering structure risk minimization. Further, to save the computational cost, an intelligent sampling strategy is applied to generate sample points at the stage of design of experiment (DOE). In this paper, a cylinder, a full vehicle frontal collision is involved. The results demonstrate that the proposed metamodel-based optimization is efficient and effective in solving crashworthiness, design optimization problems.

Wang, Hu; Li, Enying; Li, G. Y.

2011-03-01

500

Optimal solution error covariance in highly nonlinear problems of variational data assimilation  

NASA Astrophysics Data System (ADS)

The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

Shutyaev, V.; Gejadze, I.; Copeland, G. J. M.; Le Dimet, F.-X.

2012-03-01