Variational Analysis And Applications

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Variational Analysis and Applications

Boris S. Mordukhovich
Variational Analysis and Applications Book PDF

Author : Boris S. Mordukhovich
Publisher : Springer
Page : 622 pages
File Size : 52,7 Mb
Release : 2018-08-02
Category : Mathematics
ISBN : 9783319927756

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Variational Analysis and Applications by Boris S. Mordukhovich Pdf

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

R. Tyrrell Rockafellar,Roger J.-B. Wets
Variational Analysis Book PDF

Author : R. Tyrrell Rockafellar,Roger J.-B. Wets
Publisher : Springer Science & Business Media
Page : 736 pages
File Size : 48,8 Mb
Release : 2009-06-26
Category : Mathematics
ISBN : 9783642024313

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Variational Analysis by R. Tyrrell Rockafellar,Roger J.-B. Wets Pdf

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.

Variational Analysis of Regular Mappings

Alexander D. Ioffe
Variational Analysis of Regular Mappings Book PDF

Author : Alexander D. Ioffe
Publisher : Springer
Page : 495 pages
File Size : 55,5 Mb
Release : 2017-10-26
Category : Mathematics
ISBN : 9783319642772

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Variational Analysis of Regular Mappings by Alexander D. Ioffe Pdf

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

Jonathan Borwein,Qiji Zhu
Techniques of Variational Analysis Book PDF

Author : Jonathan Borwein,Qiji Zhu
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 43,8 Mb
Release : 2006-06-18
Category : Mathematics
ISBN : 9780387282718

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Techniques of Variational Analysis by Jonathan Borwein,Qiji Zhu Pdf

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

Variational Analysis and Generalized Differentiation I

Boris S. Mordukhovich
Variational Analysis and Generalized Differentiation I Book PDF

Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
Page : 598 pages
File Size : 41,8 Mb
Release : 2006-08-08
Category : Mathematics
ISBN : 9783540312475

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Variational Analysis and Generalized Differentiation I by Boris S. Mordukhovich Pdf

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.

Variational Analysis and Generalized Differentiation II

Boris S. Mordukhovich
Variational Analysis and Generalized Differentiation II Book PDF

Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
Page : 630 pages
File Size : 55,5 Mb
Release : 2006-03-02
Category : Mathematics
ISBN : 9783540312468

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Variational Analysis and Generalized Differentiation II by Boris S. Mordukhovich Pdf

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.

Optimization, Variational Analysis and Applications

Vivek Laha,Pierre Maréchal,S. K. Mishra
Optimization Variational Analysis and Applications Book PDF

Author : Vivek Laha,Pierre Maréchal,S. K. Mishra
Publisher : Springer Nature
Page : 441 pages
File Size : 52,9 Mb
Release : 2021-07-27
Category : Mathematics
ISBN : 9789811618192

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Optimization, Variational Analysis and Applications by Vivek Laha,Pierre Maréchal,S. K. Mishra Pdf

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 Set Optimization

Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Variational Analysis and Set Optimization Book PDF

Author : Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Publisher : CRC Press
Page : 226 pages
File Size : 53,8 Mb
Release : 2019-06-07
Category : Business & Economics
ISBN : 9781351712064

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Variational Analysis and Set Optimization by Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer Pdf

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

Franco Giannessi,Antonino Maugeri
Variational Analysis and Applications Book PDF

Author : Franco Giannessi,Antonino Maugeri
Publisher : Springer Science & Business Media
Page : 1163 pages
File Size : 42,6 Mb
Release : 2007-03-06
Category : Mathematics
ISBN : 9780387242767

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Variational Analysis and Applications by Franco Giannessi,Antonino Maugeri Pdf

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.

Computational Mathematics and Variational Analysis

Nicholas J. Daras,Themistocles M. Rassias
Computational Mathematics and Variational Analysis Book PDF

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Page : 564 pages
File Size : 44,9 Mb
Release : 2020-06-06
Category : Mathematics
ISBN : 9783030446253

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Computational Mathematics and Variational Analysis by Nicholas J. Daras,Themistocles M. Rassias Pdf

This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.

Implicit Functions and Solution Mappings

Asen L. Dontchev,R. Tyrrell Rockafellar
Implicit Functions and Solution Mappings Book PDF

Author : Asen L. Dontchev,R. Tyrrell Rockafellar
Publisher : Springer
Page : 466 pages
File Size : 52,5 Mb
Release : 2014-06-18
Category : Mathematics
ISBN : 9781493910373

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Implicit Functions and Solution Mappings by Asen L. Dontchev,R. Tyrrell Rockafellar Pdf

The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.

Variational Methods in Nonlinear Analysis

Dimitrios C. Kravvaritis,Athanasios N. Yannacopoulos
Variational Methods in Nonlinear Analysis Book PDF

Author : Dimitrios C. Kravvaritis,Athanasios N. Yannacopoulos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 384 pages
File Size : 53,7 Mb
Release : 2020-04-06
Category : Mathematics
ISBN : 9783110647457

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Variational Methods in Nonlinear Analysis by Dimitrios C. Kravvaritis,Athanasios N. Yannacopoulos Pdf

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.

Convex Analysis and Variational Problems

Ivar Ekeland,Roger Temam
Convex Analysis and Variational Problems Book PDF

Author : Ivar Ekeland,Roger Temam
Publisher : SIAM
Page : 414 pages
File Size : 45,7 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 161197108X

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Convex Analysis and Variational Problems by Ivar Ekeland,Roger Temam Pdf

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.

Variational Analysis and Aerospace Engineering

Aldo Frediani,Bijan Mohammadi,Olivier Pironneau,Vittorio Cipolla
Variational Analysis and Aerospace Engineering Book PDF

Author : Aldo Frediani,Bijan Mohammadi,Olivier Pironneau,Vittorio Cipolla
Publisher : Springer
Page : 535 pages
File Size : 52,8 Mb
Release : 2016-12-27
Category : Mathematics
ISBN : 9783319456805

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Variational Analysis and Aerospace Engineering by Aldo Frediani,Bijan Mohammadi,Olivier Pironneau,Vittorio Cipolla Pdf

This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

Fixed Point Theory, Variational Analysis, and Optimization

Saleh Abdullah R. Al-Mezel,Falleh Rajallah M. Al-Solamy,Qamrul Hasan Ansari
Fixed Point Theory Variational Analysis and Optimization Book PDF

Author : Saleh Abdullah R. Al-Mezel,Falleh Rajallah M. Al-Solamy,Qamrul Hasan Ansari
Publisher : CRC Press
Page : 368 pages
File Size : 54,9 Mb
Release : 2014-06-03
Category : Business & Economics
ISBN : 9781482222081

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Fixed Point Theory, Variational Analysis, and Optimization by Saleh Abdullah R. Al-Mezel,Falleh Rajallah M. Al-Solamy,Qamrul Hasan Ansari Pdf

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