Variational Analysis Of Regular Mappings
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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.
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.
Fixed Point Theory Variational Analysis And Optimization
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Author : Saleh Abdullah R. Al-Mezel
language : en
Publisher: CRC Press
Release Date : 2014-06-03
Fixed Point Theory Variational Analysis And Optimization written by Saleh Abdullah R. Al-Mezel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-03 with Business & Economics categories.
Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis-fixed point theory, variational inequalities, and vector optimization-but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions invol
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 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.
Optimality Conditions Abnormal And Degenerate Problems
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Author : Aram Arutyunov
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-31
Optimality Conditions Abnormal And Degenerate Problems written by Aram Arutyunov 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 2000-10-31 with Mathematics categories.
This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Nonsmooth Equations In Optimization
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Author : Diethard Klatte
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-17
Nonsmooth Equations In Optimization written by Diethard Klatte 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 2005-12-17 with Mathematics categories.
Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
Introduction To Numerical Methods For Variational Problems
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Author : Hans Petter Langtangen
language : en
Publisher: Springer Nature
Release Date : 2019-09-26
Introduction To Numerical Methods For Variational Problems written by Hans Petter Langtangen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-26 with Mathematics categories.
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Mathematical Analysis And Its Applications
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Author : S. M. Mazhar
language : en
Publisher: Elsevier
Release Date : 2014-05-17
Mathematical Analysis And Its Applications written by S. M. Mazhar and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-17 with Mathematics categories.
Mathematical Analysis and its Applications covers the proceedings of the International Conference on Mathematical Analysis and its Applications. The book presents studies that discuss several mathematical analysis methods and their respective applications. The text presents 38 papers that discuss topics, such as approximation of continuous functions by ultraspherical series and classes of bi-univalent functions. The representation of multipliers of eigen and joint function expansions of nonlocal spectral problems for first- and second-order differential operators is also discussed. The book will be of great interest to researchers and professionals whose work involves the use of mathematical analysis.
Metric Fixed Point Theory
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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-01-04
Metric Fixed Point Theory written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Mathematics categories.
This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.