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.
Second Order Variational Analysis In Optimization Variational Stability And Control
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Author : Boris S. Mordukhovich
language : en
Publisher: Springer Nature
Release Date :
Second Order Variational Analysis In Optimization Variational Stability And Control written by Boris S. Mordukhovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Optimization Variational Analysis And Applications
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Author : Vivek Laha
language : en
Publisher:
Release Date : 2021
Optimization Variational Analysis And Applications written by Vivek Laha and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with 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.
Variational Analysis With Applications In Optimisation And Control
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Author : Savin Treanţă
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2019-08-01
Variational Analysis With Applications In Optimisation And Control written by Savin Treanţă and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-01 with Mathematics categories.
This book focuses on the calculus of variations and related applications which combine tools and methods from partial differential equations with geometrical techniques. More precisely, it is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. It provides the latest developments in multidimensional optimization and optimal control. With various examples and applications to complement and substantiate mathematical developments, the text is a valuable guide for researchers, engineers and students in the field of mathematics, and those working in operations research, optimal control science, artificial intelligence, management science and economics.
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 And Applications
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Author : Boris Sholimovich Mordukhovich
language : en
Publisher:
Release Date : 2018
Variational Analysis And Applications written by Boris Sholimovich Mordukhovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Calculus of variations 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.--
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. This second edition covers several new topics: new section on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity; increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations; new section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem; new subsection on stochastic homogenization establishes the mathematical tools coming from ergodic theory; and an entirely new and comprehensive chapter (17) devoted to gradient flows and the dynamical approach to equilibria. The book is intended for Ph.D. students, researchers, and practitioners who want to approach the field of variational analysis in a systematic way.
Variational Analysis And Generalized Differentiation In Optimization And Control
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Author : Regina S. Burachik
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25
Variational Analysis And Generalized Differentiation In Optimization And Control written by Regina S. Burachik 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 2010-11-25 with Mathematics categories.
This book presents some 20 papers describing recent developments in advanced variational analysis, optimization, and control systems, especially those based on modern variational techniques and tools of generalized differentiation.
