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Other titles in the Springer Optimization and Its Applications series:

Springer Optimization and Its Applications #8: Set-Valued Mappings and Enlargements of Monotone Operators

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Synopses & Reviews

Publisher Comments:

Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book. The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithms. Audience This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students in pure and applied mathematics, mathematical economics, operations research and related areas. The only requisites, besides a minimum level of mathematical maturity, are some basic results of general topology and functional analysis.

Synopsis:

This is the first comprehensive book treatment of the emerging subdiscipline of set-valued mapping and enlargements of maximal monotone operators. It features several important new results and applications in the field. Throughout the text, examples help readers make the bridge from theory to application. Numerous exercises are also offered to enable readers to apply and build their own skills and knowledge.

Table of Contents

List of Figures.- Dedication.- Acknowledgments.- Preface.- Introduction.- Set Convergence and Point-to-Set Mappings.- Convex Analysis and Fixed Point Theorems.- Maximal Monotone Operators.- 5. Enlargements of Monotone Operators.- Recent Topics in Proximal Theory.- Bibliography.- Notation.- Index.

Product Details

ISBN:
9781441943460
Author:
Burachik, Regina S.
Publisher:
Springer
Author:
Iusem, Alfredo N.
Subject:
Linear Programming
Subject:
Convex
Subject:
Proximal Point
Subject:
Set-Valued
Subject:
OPTIMIZATION
Subject:
Operator theory
Subject:
Operations Research, Mathematical Programming
Subject:
Operations Research/Decision Theory
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Analysis
Subject:
Operations Research, Management Science
Subject:
Analysis <P>This work offers the first comprehensive treatment in book form of the fairly new subdiscipline in set-valued analysis of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, wi
Subject:
Mathematics-Computer
Subject:
Applied
Subject:
Operation Research/Decision Theory
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2008
Series:
Springer Optimization and Its Applications
Series Volume:
8
Publication Date:
20101129
Binding:
TRADE PAPER
Language:
English
Pages:
308
Dimensions:
235 x 155 mm 469 gr

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Springer Optimization and Its Applications #8: Set-Valued Mappings and Enlargements of Monotone Operators New Trade Paper
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Product details 308 pages Not Avail - English 9781441943460 Reviews:
"Synopsis" by , This is the first comprehensive book treatment of the emerging subdiscipline of set-valued mapping and enlargements of maximal monotone operators. It features several important new results and applications in the field. Throughout the text, examples help readers make the bridge from theory to application. Numerous exercises are also offered to enable readers to apply and build their own skills and knowledge.
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