Set-Valued Mappings and Enlargements of Monotone Operators / Edition 1 by Regina Burachik, Alfredo N. Iusem | | 9780387697550 | Hardcover | Barnes & Noble
Set-Valued Mappings and Enlargements of Monotone Operators / Edition 1

Set-Valued Mappings and Enlargements of Monotone Operators / Edition 1

by Regina Burachik, Alfredo N. Iusem
     
 

ISBN-10: 0387697551

ISBN-13: 9780387697550

Pub. Date: 10/28/2007

Publisher: Springer US

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

Overview

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.

Product Details

ISBN-13:
9780387697550
Publisher:
Springer US
Publication date:
10/28/2007
Series:
Springer Optimization and Its Applications Series, #8
Edition description:
2008
Pages:
294
Product dimensions:
6.10(w) x 9.25(h) x 0.04(d)

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.

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