Optimization Variational Analysis And Applications
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Variational Analysis And Applications
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Author : Boris S. Mordukhovich
language : en
Publisher: Springer
Release Date : 2018-08-02
Variational Analysis And Applications written by Boris S. Mordukhovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Mathematics categories.
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.
Optimization Variational Analysis And Applications
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Author : Vivek Laha
language : en
Publisher: Springer Nature
Release Date : 2021-07-27
Optimization Variational Analysis And Applications written by Vivek Laha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-27 with Mathematics categories.
This book includes selected papers presented at the Indo-French Seminar on Optimization, Variational Analysis and Applications (IFSOVAA-2020), held at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, from 2–4 February 2020. The book discusses current optimization problems and their solutions by using the powerful tool of variational analysis. Topics covered in this volume include set optimization, multiobjective optimization, mathematical programs with complementary, equilibrium, vanishing and switching constraints, copositive optimization, interval-valued optimization, sequential quadratic programming, bound-constrained optimization, variational inequalities, and more. Several applications in different branches of applied mathematics, engineering, economics, finance, and medical sciences have been included. Each chapter not only provides a detailed survey of the topic but also builds systematic theories and suitable algorithms to deduce the most recent findings in literature. This volume appeals to graduate students as well as researchers and practitioners in pure and applied mathematics and related fields that make use of variational analysis in solving optimization problems.
Variational Analysis And Applications
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Author : Franco Giannessi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-06
Variational Analysis And Applications written by Franco Giannessi 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 2007-03-06 with Mathematics categories.
This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.
Vector Optimization
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Author : Guang-ya Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-20
Vector Optimization written by Guang-ya Chen 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 2005-11-20 with Business & Economics categories.
Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solu tion in 1896). Typical examples of vector optimization model include maxi mization/minimization of the objective pairs (time, cost), (benefit, cost), and (mean, variance) etc. Many practical equilibrium problems can be formulated as variational in equality problems, rather than optimization problems, unless further assump tions are imposed. The vector variational inequality was introduced by Gi- nessi (1980). Extensive research on its relations with vector optimization, the existence of a solution and duality theory has been pursued. The fundamental idea of the Ekeland's variational principle is to assign an optimization problem a slightly perturbed one having a unique solution which is at the same time an approximate solution of the original problem. This principle has been an important tool for nonlinear analysis and optimization theory. Along with the development of vector optimization and set-valued optimization, the vector variational principle introduced by Nemeth (1980) has been an interesting topic in the last decade. Fan Ky's minimax theorems and minimax inequalities for real-valued func tions have played a key role in optimization theory, game theory and math ematical economics. An extension was proposed to vector payoffs was intro duced by Blackwell (1955).
Variational Analysis And Set Optimization
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Author : Akhtar A. Khan
language : en
Publisher: CRC Press
Release Date : 2019-06-07
Variational Analysis And Set Optimization written by Akhtar A. Khan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-07 with Business & Economics categories.
This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.
Variational Analysis
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Author : R. Tyrrell Rockafellar
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-26
Variational Analysis written by R. Tyrrell Rockafellar 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 2009-06-26 with Mathematics categories.
From its origins in the minimization of integral functionals, the notion of 'variations' has evolved greatly in connection with applications in optimization, equilibrium, and control. It refers not only to constrained movement away from a point, but also to modes of perturbation and approximation that are best describable by 'set convergence', variational convergence of functions and the like. This book develops a unified framework and, in finite dimension, provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, maximal monotone mappings, second-order subderivatives, measurable selections and normal integrands. The changes in this 3rd printing mainly concern various typographical corrections, and reference omissions that came to light in the previous printings. Many of these reached the authors' notice through their own re-reading, that of their students and a number of colleagues mentioned in the Preface. The authors also included a few telling examples as well as improved a few statements, with slightly weaker assumptions or have strengthened the conclusions in a couple of instances.
Variational Analysis In Sobolev And Bv Spaces
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Author : Hedy Attouch
language : en
Publisher: SIAM
Release Date : 2014-10-02
Variational Analysis In Sobolev And Bv Spaces written by Hedy Attouch and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-02 with Mathematics categories.
This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision.
Variational Analysis Of Regular Mappings
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Author : Alexander D. Ioffe
language : en
Publisher: Springer
Release Date : 2017-10-26
Variational Analysis Of Regular Mappings written by Alexander D. Ioffe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Mathematics categories.
This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.
Techniques Of Variational Analysis
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Author : Jonathan Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18
Techniques Of Variational Analysis written by Jonathan Borwein 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 2006-06-18 with Mathematics categories.
Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis Provides a good introduction to the topic
Convex Analysis And Variational Problems
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Author : Ivar Ekeland
language : en
Publisher: SIAM
Release Date : 1999-12-01
Convex Analysis And Variational Problems written by Ivar Ekeland and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.
This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.