Variational Analysis In Sobolev And Bv Spaces
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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 In Sobolev And Bv Spaces
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Battery Reconditioning
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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.
Unilateral Variational Analysis In Banach Spaces In 2 Parts
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Author : Lionel Thibault
language : en
Publisher: World Scientific
Release Date : 2023-02-14
Unilateral Variational Analysis In Banach Spaces In 2 Parts written by Lionel Thibault and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-14 with Mathematics categories.
The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems.The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments.Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.
Lectures On Variational Analysis
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Author : Asen L. Dontchev
language : en
Publisher: Springer Nature
Release Date : 2022-02-04
Lectures On Variational Analysis written by Asen L. Dontchev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-04 with Mathematics categories.
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
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.
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.
Functional Analysis And Applied Optimization In Banach Spaces
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Author : Fabio Botelho
language : en
Publisher: Springer
Release Date : 2014-06-12
Functional Analysis And Applied Optimization In Banach Spaces written by Fabio Botelho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Mathematics categories.
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Variational Methods In Nonlinear Analysis
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Author : Dimitrios C. Kravvaritis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-04-06
Variational Methods In Nonlinear Analysis written by Dimitrios C. Kravvaritis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-06 with Mathematics categories.
This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
Sobolev Spaces
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Author : Vladimir Maz'ya
language : en
Publisher: Springer
Release Date : 2013-12-21
Sobolev Spaces written by Vladimir Maz'ya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.
The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q
Convex Analysis And Monotone Operator Theory In Hilbert Spaces
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Author : Heinz H. Bauschke
language : en
Publisher: Springer
Release Date : 2017-02-28
Convex Analysis And Monotone Operator Theory In Hilbert Spaces written by Heinz H. Bauschke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-28 with Mathematics categories.
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.