Post Optimal Analysis In Linear Semi Infinite Optimization

Author : Miguel A. Goberna,Marco A. López
Publisher : Springer Science & Business Media
Page : 128 pages
File Size : 41,5 Mb
Release : 2014-01-06
Category : Business & Economics
ISBN : 9781489980441

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Post-Optimal Analysis in Linear Semi-Infinite Optimization by Miguel A. Goberna,Marco A. López Pdf

Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

Author : Miguel A. Goberna,Marco A. Lopez
Publisher : Unknown
Page : 132 pages
File Size : 44,5 Mb
Release : 2014-01-31
Category : Electronic
ISBN : 1489980458

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Post-Optimal Analysis in Linear Semi-Infinite Optimization by Miguel A. Goberna,Marco A. Lopez Pdf

Author : Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 46,7 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9780387894966

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Optimization and Optimal Control by Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj Pdf

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.

Author : Rembert Reemtsen,Jan-J. Rückmann
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 43,5 Mb
Release : 1998-04-30
Category : Computers
ISBN : 0792350545

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Semi-Infinite Programming by Rembert Reemtsen,Jan-J. Rückmann Pdf

Semi-infinite programming (briefly: SIP) is an exciting part of mathematical programming. SIP problems include finitely many variables and, in contrast to finite optimization problems, infinitely many inequality constraints. Prob lems of this type naturally arise in approximation theory, optimal control, and at numerous engineering applications where the model contains at least one inequality constraint for each value of a parameter and the parameter, repre senting time, space, frequency etc., varies in a given domain. The treatment of such problems requires particular theoretical and numerical techniques. The theory in SIP as well as the number of numerical SIP methods and appli cations have expanded very fast during the last years. Therefore, the main goal of this monograph is to provide a collection of tutorial and survey type articles which represent a substantial part of the contemporary body of knowledge in SIP. We are glad that leading researchers have contributed to this volume and that their articles are covering a wide range of important topics in this subject. It is our hope that both experienced students and scientists will be well advised to consult this volume. We got the idea for this volume when we were organizing the semi-infinite pro gramming workshop which was held in Cottbus, Germany, in September 1996.

Author : K. Glashoff,S.-A. Gustafson
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461211426

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Linear Optimization and Approximation by K. Glashoff,S.-A. Gustafson Pdf

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Author : José M. Amigó,María J. Cánovas,Marco A. López-Cerdá,Manuel López-Pellicer
Publisher : Springer Nature
Page : 273 pages
File Size : 53,7 Mb
Release : 2023-07-01
Category : Mathematics
ISBN : 9783031300141

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Functional Analysis and Continuous Optimization by José M. Amigó,María J. Cánovas,Marco A. López-Cerdá,Manuel López-Pellicer Pdf

The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.

Author : Rafael Correa,Abderrahim Hantoute,Marco A. López
Publisher : Springer Nature
Page : 451 pages
File Size : 55,7 Mb
Release : 2023-07-11
Category : Business & Economics
ISBN : 9783031295515

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Fundamentals of Convex Analysis and Optimization by Rafael Correa,Abderrahim Hantoute,Marco A. López Pdf

This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.

Author : Boris S. Mordukhovich
Publisher : Springer
Page : 622 pages
File Size : 47,7 Mb
Release : 2018-08-02
Category : Mathematics
ISBN : 9783319927756

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Variational Analysis and Applications by Boris S. Mordukhovich Pdf

Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.

Author : Miguel A. Goberna,Marco A. López
Publisher : Unknown
Page : 380 pages
File Size : 51,6 Mb
Release : 1998-03-11
Category : Mathematics
ISBN : STANFORD:36105021159616

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Linear Semi-Infinite Optimization by Miguel A. Goberna,Marco A. López Pdf

A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.

Author : Oliver Stein
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 51,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781441991645

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Bi-Level Strategies in Semi-Infinite Programming by Oliver Stein Pdf

Semi-infinite optimization is a vivid field of active research. Recently semi infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.

Author : K. Glashoff,S.-A. Gustafson
Publisher : Springer
Page : 212 pages
File Size : 45,6 Mb
Release : 1983-04-13
Category : Science
ISBN : 0387908579

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Linear Optimization and Approximation by K. Glashoff,S.-A. Gustafson Pdf

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Author : Elijah Polak
Publisher : Springer Science & Business Media
Page : 801 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206637

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Optimization by Elijah Polak Pdf

This book deals with optimality conditions, algorithms, and discretization tech niques for nonlinear programming, semi-infinite optimization, and optimal con trol problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of con sistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth prob lems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algo rithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, estab lishing optimality conditions for highly complex problems, such as optimal con trol problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent.

Author : Tomas Gal
Publisher : Walter de Gruyter
Page : 465 pages
File Size : 44,5 Mb
Release : 2010-09-03
Category : Computers
ISBN : 9783110871203

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Postoptimal Analyses, Parametric Programming, and Related Topics by Tomas Gal Pdf

Postoptimal Analyses, Parametric Programming, and Related Topics: Degeneracy, Multicriteria Decision Making Redundancy.

Author : Aharon Ben-Tal,Laurent El Ghaoui,Arkadi Nemirovski
Publisher : Princeton University Press
Page : 576 pages
File Size : 41,7 Mb
Release : 2009-08-10
Category : Mathematics
ISBN : 9781400831050

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Robust Optimization by Aharon Ben-Tal,Laurent El Ghaoui,Arkadi Nemirovski Pdf

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Author : Saul I. Gass,Carl M. Harris
Publisher : Springer Science & Business Media
Page : 969 pages
File Size : 45,7 Mb
Release : 2001
Category : Management science
ISBN : 9780792378273

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Encyclopedia of Operations Research and Management Science by Saul I. Gass,Carl M. Harris Pdf

Audience: Anyone concerned with the science, techniques and ideas of how decisions are made."--BOOK JACKET.