Combined Relaxation Methods For Variational Inequalities by Igor Konnov

Combined Relaxation Methods For Variational Inequalities

byIgor Konnov

Paperback | October 18, 2000

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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.
Title:Combined Relaxation Methods For Variational InequalitiesFormat:PaperbackProduct dimensions:196 pages, 9.25 X 6.1 X 0 inShipping dimensions:196 pages, 9.25 X 6.1 X 0 inPublished:October 18, 2000Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540679995

ISBN - 13:9783540679998

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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