ISBN-10:
3540679995
ISBN-13:
9783540679998
Pub. Date:
11/27/2000
Publisher:
Springer Berlin Heidelberg
Combined Relaxation Methods for Variational Inequalities / Edition 1

Combined Relaxation Methods for Variational Inequalities / Edition 1

by Igor Konnov

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Overview

Combined Relaxation Methods for Variational Inequalities / Edition 1

Variational inequalities proved to be a very useful and powerful tool for in­ vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. In fact, varia­ tional inequalities for example provide a unifying framework for the study of such diverse problems as boundary value problems, price equilibrium prob­ lems and traffic network equilibrium problems. Besides, they are closely re­ lated with many general problems of Nonlinear Analysis, such as fixed point, optimization and complementarity problems. As a result, the theory and so­ lution methods for variational inequalities have been studied extensively, and considerable advances have been made in these areas. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relax­ ation (CR) approach. This approach is based on combining, modifying and generalizing ideas contained in various relaxation methods. In fact, each com­ bined relaxation method has a two-level structure, i.e., a descent direction and a stepsize at each iteration are computed by finite relaxation procedures.

Product Details

ISBN-13: 9783540679998
Publisher: Springer Berlin Heidelberg
Publication date: 11/27/2000
Series: Lecture Notes in Economics and Mathematical Systems , #495
Edition description: 2001
Pages: 184
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Notation and Convention.- Variational Inequalities with Continuous Mappings.- Problem Formulation and Basic Facts; Main Idea of CR Methods; Implementable CR Methods; Modified Rules for Computing Iteration Parameters; CR Method Based on a Frank-Wolfe Type Auxiliary Procedure; CR Method for Variational Inequalities with Nonlinear Constraints; Variational Inequalities with Multivalued Mappings.- Problem Formulation and Basic Facts; CR Method for the Mixed Variational Inequality Problem; CR Method for the Generalized Variational Inequality Problem; CR Method for Multivalued Inclusions; Decomposable CR Method; Applications and Numerical Experiments.- Iterative Methods for Variational Inequalities with non Strictly Monotone Mappings; Economic Equilibrium Problems; Numerical Experiments with Test Problems; Auxiliary Results.- Feasible Quasi-Nonexpansive Mappings; Error Bounds for Linearly Constrained Problems; A Relaxation Subgradient Method Without Linesearch

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