Vector Optimization With Infimum And Supremum

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Vector Optimization With Infimum And Supremum

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Author : Andreas Löhne
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-25

Vector Optimization With Infimum And Supremum written by Andreas Löhne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-25 with Business & Economics categories.

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.

Recent Developments In Vector Optimization

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Author : Qamrul Hasan Ansari
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-21

Recent Developments In Vector Optimization written by Qamrul Hasan Ansari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-21 with Business & Economics categories.

We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

Mathematics Of Optimization Smooth And Nonsmooth Case

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Author : Giorgio Giorgi
language : en
Publisher: Elsevier
Release Date : 2004-03-10

Mathematics Of Optimization Smooth And Nonsmooth Case written by Giorgio Giorgi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-10 with Mathematics categories.

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems. The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature. Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems. · Self-contained · Clear style and results are either proved or stated precisely with adequate references · The authors have several years experience in this field · Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems · Useful long references list at the end of each chapter

Variational Methods In Partially Ordered Spaces

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Author : Alfred Göpfert
language : en
Publisher: Springer Nature
Release Date : 2023-12-08

Variational Methods In Partially Ordered Spaces written by Alfred Göpfert and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-08 with Business & Economics categories.

This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.

Vector Optimization

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Author : Johannes Jahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-22

Vector Optimization written by Johannes Jahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-22 with Business & Economics categories.

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning. This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.

Set Valued Optimization

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Author : Akhtar A. Khan
language : en
Publisher: Springer
Release Date : 2014-10-20

Set Valued Optimization written by Akhtar A. Khan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-20 with Mathematics categories.

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.

Set Optimization And Applications The State Of The Art

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Author : Andreas H Hamel
language : en
Publisher: Springer
Release Date : 2015-11-21

Set Optimization And Applications The State Of The Art written by Andreas H Hamel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-21 with Mathematics categories.

This volume presents five surveys with extensive bibliographies and six original contributions on set optimization and its applications in mathematical finance and game theory. The topics range from more conventional approaches that look for minimal/maximal elements with respect to vector orders or set relations, to the new complete-lattice approach that comprises a coherent solution concept for set optimization problems, along with existence results, duality theorems, optimality conditions, variational inequalities and theoretical foundations for algorithms. Modern approaches to scalarization methods can be found as well as a fundamental contribution to conditional analysis. The theory is tailor-made for financial applications, in particular risk evaluation and [super-]hedging for market models with transaction costs, but it also provides a refreshing new perspective on vector optimization. There is no comparable volume on the market, making the book an invaluable resource for researchers working in vector optimization and multi-criteria decision-making, mathematical finance and economics as well as [set-valued] variational analysis.

Mathematical Optimization Theory And Operations Research

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Author : Igor Bykadorov
language : en
Publisher: Springer Nature
Release Date : 2019-10-26

Mathematical Optimization Theory And Operations Research written by Igor Bykadorov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-26 with Computers categories.

This book constitutes revised and selected papers from the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019. The 40 full papers and 4 short papers presented in this volume were carefully reviewed and selected from a total of 170 submissions. The papers in the volume are organised according to the following topical headings: ​combinatorial optimization; game theory and mathematical economics; data mining and computational geometry; integer programming; mathematical programming; operations research; optimal control and applications.

Vector Optimization

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Author : Johannes Jahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05

Vector Optimization written by Johannes Jahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Business & Economics categories.

In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization.

Duality In Vector Optimization

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Author : Radu Ioan Bot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-12

Duality In Vector Optimization written by Radu Ioan Bot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-12 with Mathematics categories.

This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.