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Asymptotic Cones and Functions in Optimization and Variational Inequalities (Springer Monographs in Mathematics)

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Synopses & Reviews

Publisher Comments:

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. 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. 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.

Synopsis:

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.

Synopsis:

Includes bibliographical references (p. [233]-242) and index.

Table of Contents

Convex Analysis and Set Valued Maps: A Review * Asymptotic Cones and Functions * Existence and Stability in Optimization Problems * Minimizing and Stationary Sequences * Duality in Optimization Problems * Maximal Monotone Maps and Variational Inequalities

Product Details

ISBN:
9780387955209
Author:
Auslender, A.
Publisher:
Springer
Author:
Auslender, Alfred
Author:
Teboulle, Marc
Author:
Teboulle, M.
Location:
New York, NY
Subject:
General
Subject:
Calculus
Subject:
Linear Programming
Subject:
Mathematical optimization
Subject:
Convex programming
Subject:
Convex functions
Subject:
Variational inequalities
Subject:
Variational inequalities (Mathematics)
Subject:
Mathematics-Calculus
Subject:
asymptotic cones
Subject:
asymptotic functions
Subject:
asymptotic sets
Subject:
Nonlinear programming
Subject:
OPTIMIZATION
Subject:
Optimization Theory
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Operations Research, Management Science
Subject:
Operations Research/Decision Theory
Subject:
Operation Research/Decision Theory
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Operations Research
Copyright:
Edition Description:
Book
Series:
Springer Monographs in Mathematics
Series Volume:
107-211
Publication Date:
20021001
Binding:
Paperback
Language:
English
Pages:
261
Dimensions:
235 x 155 mm 500 gr

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Asymptotic Cones and Functions in Optimization and Variational Inequalities (Springer Monographs in Mathematics) New Hardcover
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Product details 261 pages Springer-Verlag - English 9780387955209 Reviews:
"Synopsis" by , 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.
"Synopsis" by , Includes bibliographical references (p. [233]-242) and index.
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