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Asymptotic Cones and Functions in Optimization and Variational Inequalities (Springer Monographs in Mathematics) 🔍
Alfred Auslender, Marc Teboulle (auth.) Springer-Verlag New York, Springer Monographs in Mathematics, Springer Monographs in Mathematics, 1, 2003
英语 [en] · PDF · 2.3MB · 2003 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
Nonlinear applied analysis and in particular the related ?elds of continuous optimization and variational inequality problems have gone through major developments over the last three decades and have reached maturity. A pivotal role in these developments has been played by convex analysis, a rich area covering a broad range of problems in mathematical sciences and its applications. Separation of convex sets and the Legendre–Fenchel conjugate transforms are fundamental notions that have laid the ground for these fruitful developments. Two other fundamental notions that have contributed to making convex analysis a powerful analytical tool and that haveoftenbeenhiddeninthesedevelopmentsarethenotionsofasymptotic sets and functions. The purpose of this book is to provide a systematic and comprehensive account of asymptotic sets and functions, from which a broad and u- ful theory emerges in the areas of optimization and variational inequa- ties. There is a variety of motivations that led mathematicians to study questions revolving around attaintment of the in?mum in a minimization problem and its stability, duality and minmax theorems, convexi?cation of sets and functions, and maximal monotone maps. In all these topics we are faced with the central problem of handling unbounded situations.
Erscheinungsdatum: 01.10.2002
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lgrsnf/A:\compressed\10.1007%2Fb97594.pdf
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nexusstc/Asymptotic Cones and Functions in Optimization and Variational Inequalities/a473e6fd9a739ecb857bfaa61e28bdce.pdf
备用文件名
scihub/10.1007/b97594.pdf
备用文件名
zlib/Mathematics/Alfred Auslender, Marc Teboulle (auth.)/Asymptotic Cones and Functions in Optimization and Variational Inequalities_2105472.pdf
备选作者
Alfred Auslender, Marc Teboulle, A. Auslender
备选作者
Auslender, Alfred, Teboulle, Marc
备用出版商
Springer London, Limited
备用出版商
Springer Nature
备用出版商
Springer US
备用出版商
Copernicus
备用出版商
Telos
备用版本
Springer monographs in mathematics, New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo, 2003
备用版本
Springer monographs in mathematics, New York, New York State, 2003
备用版本
United States, United States of America
备用版本
Springer Nature, New York, 2003
备用版本
October 1, 2002
备用版本
1, 20060507
备用版本
2003, 2002
元数据中的注释
sm41119201
元数据中的注释
{"container_title":"Springer Monographs in Mathematics","edition":"1","isbns":["0387225900","0387955208","9780387225906","9780387955209"],"last_page":249,"publisher":"Springer","series":"Springer Monographs in Mathematics"}
元数据中的注释
Includes bibliographical references and index.
备用描述
<p><p>this Book Provides A Systematic And Comprehensive Account Of Asymptotic Sets And Functions From Which A Broad And Useful Theory Emerges In The Areas Of Optimization And Variational Inequalities. A Variety Of Motivations Leads Mathematicians To Study Questions About Attainment Of The Infimum In A Minimization Problem And Its Stability, Duality And Minmax Theorems, Convexification Of Sets And Functions, And Maximal Monotone Maps. For Each There Is The Central Problem Of Handling Unbounded Situations. Such Problems Arise In Theory But Also Within The Development Of Numerical Methods.<p>the Book Focuses On The Notions Of Asymptotic Cones And Associated Asymptotic Functions That Provide A Natural And Unifying Framework For The Resolution Of These Types Of Problems. These Notions Have Been Used Largely And Traditionally In Convex Analysis, Yet These Concepts Play A Prominent And Independent Role In Both Convex And Nonconvex Analysis. This Book Covers Convex And Nonconvex Problems, Offering Detailed Analysis And Techniques That Go Beyond Traditional Approaches.<p>the Book Will Serve As A Useful Reference And Self-contained Text For Researchers And Graduate Students In The Fields Of Modern Optimization Theory And Nonlinear Analysis.</p>
备用描述
This book provides a systematic and comprehensive account of asymptotic sets and functions from which a broad and useful theory emerges in the areas of optimization and variational inequalities. Mainly it is concerned with the existence of solutions of a given problem in these classes, whenever for example standard compacity hypothesis is not present. Thus it addresses the central problem of handling unbounded situations. This book will be useful to advanced graduate students, researchers, and practitioners in the fields of optimization theory, nonlinear programming, and applied mathematical sciences
备用描述
This systematic and comprehensive account of asymptotic sets and functions develops a broad and useful theory in the areas of optimization and variational inequalities. The central focus is on problems of handling unbounded situations, using solutions of a given problem in these classes, when for example standard compacity hypothesis is not present. This book will interest advanced graduate students, researchers, and practitioners of optimization theory, nonlinear programming, and applied mathematics.
备用描述
Convex Analysis and Set-Valued Maps: A Review....Pages 1-24
Asymptotic Cones and Functions....Pages 25-80
Existence and Stability in Optimization Problems....Pages 81-118
Minimizing and Stationary Sequences....Pages 119-144
Duality in Optimization Problems....Pages 145-182
Maximal Monotone Maps and Variational Inequalities....Pages 183-232
备用描述
"The book will serve as useful reference and self-contained text for researchers and graduate students in the fields of modern optimization theory and nonlinear analysis."--BOOK JACKET.
备用描述
Convexity plays a fundamental role in the analysis of optimization problems.
开源日期
2013-08-01
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