Optimization Variational Analysis And Applications

Author : Vivek Laha,Pierre Maréchal,S. K. Mishra
Publisher : Springer Nature
Page : 441 pages
File Size : 55,5 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.

Author : Boris S. Mordukhovich
Publisher : Springer
Page : 622 pages
File Size : 47,5 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.

Author : Franco Giannessi,Antonino Maugeri
Publisher : Springer Science & Business Media
Page : 1163 pages
File Size : 46,5 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.

Author : Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Publisher : CRC Press
Page : 324 pages
File Size : 50,7 Mb
Release : 2019-06-07
Category : Business & Economics
ISBN : 9781351712071

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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.

Author : Vivek Laha,Pierre Maréchal,S. K. Mishra
Publisher : Unknown
Page : 0 pages
File Size : 50,5 Mb
Release : 2021
Category : Electronic
ISBN : 9811618208

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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.

Author : Boris S. Mordukhovich
Publisher : Springer
Page : 0 pages
File Size : 48,8 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 3031534751

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Second-Order Variational Analysis in Optimization, Variational Stability, and Control by Boris S. Mordukhovich Pdf

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.

Author : Regina S. Burachik,Jen-Chih Yao
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 42,9 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9781441904379

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Variational Analysis and Generalized Differentiation in Optimization and Control by Regina S. Burachik,Jen-Chih Yao Pdf

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.

Author : Savin Treanţă
Publisher : Cambridge Scholars Publishing
Page : 186 pages
File Size : 51,9 Mb
Release : 2019-08-01
Category : Mathematics
ISBN : 9781527537859

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Variational Analysis with Applications in Optimisation and Control by Savin Treanţă Pdf

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.

Author : Boris Sholimovich Mordukhovich
Publisher : Unknown
Page : 128 pages
File Size : 43,5 Mb
Release : 2018
Category : Calculus of variations
ISBN : 3319927744

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Variational Analysis and Applications by Boris Sholimovich 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.--

Author : Jonathan Borwein,Qiji Zhu
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 52,8 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

Author : Hedy Attouch,Giuseppe Buttazzo,Gerard Michaille
Publisher : SIAM
Page : 794 pages
File Size : 50,7 Mb
Release : 2014-10-02
Category : Mathematics
ISBN : 9781611973471

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Variational Analysis in Sobolev and BV Spaces by Hedy Attouch,Giuseppe Buttazzo,Gerard Michaille Pdf

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.

Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
Page : 630 pages
File Size : 53,7 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.

Author : Asen L. Dontchev
Publisher : Springer Nature
Page : 223 pages
File Size : 53,7 Mb
Release : 2022-02-04
Category : Mathematics
ISBN : 9783030799113

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Lectures on Variational Analysis by Asen L. Dontchev Pdf

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.

Author : R. Tyrrell Rockafellar,Roger J.-B. Wets
Publisher : Springer Science & Business Media
Page : 736 pages
File Size : 54,8 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.

Author : Anonim
Publisher : Unknown
Page : 244 pages
File Size : 48,5 Mb
Release : 2011-04-11
Category : Electronic
ISBN : 1441904387

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Variational Analysis and Generalized Differentiation in Optimization and Control by Anonim Pdf