Combined Relaxation Methods for Variational Inequa

Konnov, Igor

ISBN 10: 3540679995 / ISBN 13: 9783540679998

Published by Springer, 2000

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Bibliographic Details

• Title: Combined Relaxation Methods for Variational Inequa
• Publisher: Springer
• Publication Date: 2000
• Language: English
• ISBN 10: 3540679995
• ISBN 13: 9783540679998
• Binding: Soft cover
• Condition: Brand New

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Synopsis

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.