Variational Analysis and Generalized Differentiation I: Basic Theory / Edition 1
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Variational Analysis and Generalized Differentiation I: Basic Theory / Edition 1

by Boris S. Mordukhovich
     
 

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ISBN-10: 3540254374

ISBN-13: 9783540254379

Pub. Date: 11/12/2012

Publisher: Springer Berlin Heidelberg

Variational analysis is a fruitful area in mathematics that, on the one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. One of the most characteristic features of modern

Overview

Variational analysis is a fruitful area in mathematics that, on the one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which enters naturally not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the heart of variational analysis and its applications.

This monograph in two volumes contains a 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 and presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first of volume is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume contains various applications. Both volumes contain abundant bibliographies and extensive commentaries.

This book will be of interest to researchers and graduate students in mathematical sciences. It may also be useful to a broad range of researchers, practitioners, and graduate students involved in the study and applications of variational methods in economics, engineering, control systems, operations research, statistics, mechanics, and other applied sciences.

Product Details

ISBN-13:
9783540254379
Publisher:
Springer Berlin Heidelberg
Publication date:
11/12/2012
Series:
Grundlehren der mathematischen Wissenschaften Series, #330
Edition description:
1st ed. 2006, Corr. 2nd printing 2012
Pages:
579
Product dimensions:
8.27(w) x 11.69(h) x 0.05(d)

Table of Contents

Generalized Differentiation in Banach Spaces: Generalized Normals to Nonconvex Sets. Coderivatives of Set-Valued Mappings. Subdifferentials of Nonsmooth Functions.- Extremal Principle in Variational Analysis: Set Extremality and Nonconvex Separation. Extremal Principle in Asplund Spaces. Relations with Variational Principles. Representations and Characterizations in Asplund Spaces. Versions of the Extremal Principle in Banach Spaces.- Full Calculus in Asplund Spaces: Calculus Rules for Normals and Coderivatives. Subdifferential Calculus and Related Topics. SNC Calculus for Sets and Mappings.- Lipschitzian Stability and Sensivity Analysis: Neighborhood Criteria and Exact Bounds. Pointbased Characterizations. Sensitivity Analysis for Constraint Systems. Sensitivity Analysis for Variational Systems.- References.- Glossary of Notation.- Index of Statements.

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