Multivalued Analysis and Nonlinear Programming Problems with Perturbations / Edition 1

by B. Luderer, L. Minchenko, T. Satsura

Overview

The book presents a treatment of topological and differential properties of multivalued mappings and marginal functions. In addition, applications to sensitivity analysis of nonlinear programming problems under perturbations are studied. Properties of marginal functions associated with optimization problems are analyzed under quite general constraints defined by means of multivalued mappings. A unified approach to directional differentiability of functions and multifunctions forms the base of the volume. Nonlinear programming problems involving quasidifferentiable functions are considered as well. A significant part of the results are based on theories and concepts of two former Soviet Union researchers, Demyanov and Rubinov, and have never been published in English before.
It contains all the necessary information from multivalued analysis and does not require special knowledge, but assumes basic knowledge of calculus at an undergraduate level.

Product Details

ISBN-13:	9781402010590
Publisher:	Springer US
Publication date:	12/31/2002
Series:	Nonconvex Optimization and Its Applications , #66
Edition description:	2003
Pages:	210
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

1. Basic Notation.- 2. Basic Problems of Multivalued Analysis.- 3. Properties of Multivalued Mappings.- 4. Subdifferentials of Marginal Functions.- 5. Derivatives of Marginal Functions.- 6. Sensitivity Analysis.- Bibliographical Comments.- References.

Editorial Reviews

From the reviews:

"The aim of this book is to study infinite dimensional spaces, multivalued mappings and the associated marginal functions … . The material is presented in a clear, rigorous manner. Besides the bibliographical comments … references to the literature are given within the text. … the unified approach to the directional differentiability of multifunctions and their associated marginal functions is a remarkable feature of the book … . the book is a useful contribution to nonsmooth analysis and optimization." (Winfried Schirotzek, Zentralblatt MATH, Vol. 1061 (11), 2005)

From the Publisher