Download or read book Variational Analysis and Generalized Differentiation II written by Boris S. Mordukhovich and published by Springer Science & Business Media. This book was released on 2006-03-02 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Download or read book Variational Analysis and Generalized Differentiation I written by Boris S. Mordukhovich and published by Springer Science & Business Media. This book was released on 2006-08-08 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Download or read book Variational Analysis and Applications written by Boris S. Mordukhovich and published by Springer. This book was released on 2018-08-02 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Analysis and Generalized Differentiation written by Boris S. Mordukhovich and published by . This book was released on 2006 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Analysis and Generalized Differentiation in Optimization and Control written by Regina S. Burachik and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Analysis and Generalized Differentiation written by Boris S. Mordukhovich and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Analysis and Generalized Differentiation in Optimization and Control written by and published by . This book was released on 2011-04-11 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Analysis and Generalized Differentiation in Optimization and Control written by Regina Burachik and published by Springer. This book was released on 2010-11-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Analysis and Generalized Differentiation I written by Boris S. Mordukhovich and published by Springer. This book was released on 2012-10-28 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Download or read book Variational Analysis and Generalized Differentiation written by Boris S. Mordukhovich and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Analysis and Generalized Differentiation written by Boris S. Mordukhovich and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Analysis and Generalized Differentiation written by Boris Sholimovich Mordukhovich and published by . This book was released on 2006 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second Order Variational Analysis in Optimization Variational Stability and Control written by Boris S. Mordukhovich and published by Springer Nature. This book was released on with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second Order Variational Analysis in Optimization Variational Stability and Control written by Boris S. Mordukhovich and published by Springer. This book was released on 2024-04-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variational Analysis and Generalized Differentiation: I Basic Theory, II Applications (2006). This present book is the first entirely devoted to second-order variational analysis with numerical algorithms and applications to practical models. It covers a wide range of topics including theoretical, numerical, and implementations that will interest researchers in analysis, applied mathematics, mathematical economics, engineering, and optimization. Inclusion of a variety of exercises and commentaries in each chapter allows the book to be used effectively in a course on this subject. This area has been well recognized as an important and rapidly developing area of nonlinear analysis and optimization with numerous applications. Consisting of 9 interrelated chapters, the book is self-contained with the inclusion of some preliminaries in Chapter 1. Results presented are useful tools for characterizations of fundamental notions of variational stability of solutions for diverse classes of problems in optimization and optimal control, the study of variational convexity of extended-real-valued functions and their specifications and variational sufficiency in optimization. Explicit calculations and important applications of second-order subdifferentials associated with the achieved characterizations of variational stability and related concepts, to the design and justification of second-order numerical algorithms for solving various classes of optimization problems, nonsmooth equations, and subgradient systems, are included. Generalized Newtonian algorithms are presented that show local and global convergence with linear, superlinear, and quadratic convergence rates. Algorithms are implemented to address interesting practical problems from the fields of machine learning, statistics, imaging, and other areas.
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-07-17 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This book develops a unified framework and 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, and normal integrands.
Download or read book Optimization Variational Analysis and Applications written by Vivek Laha and published by Springer Nature. This book was released on 2021-07-27 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Unilateral Variational Analysis In Banach Spaces In 2 Parts written by Lionel Thibault and published by World Scientific. This book was released on 2023-02-14 with total page 1629 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
