Combined Relaxation Methods for Variational Inequalities

Igor Konnov

ISBN 10: 3540679995 / ISBN 13: 9783540679998

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2000, 2000

About this Item

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 200 pp. Englisch.

Seller Inventory # 9783540679998

Bibliographic Details

• Title: Combined Relaxation Methods for Variational Inequalities
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2000
• Publication Date: 2000
• Language: English
• ISBN 10: 3540679995
• ISBN 13: 9783540679998
• Binding: Taschenbuch
• Condition: Neu

About this title

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.

Product Description

Variational inequalities proved to be a very useful tool for investigation and solution of various equilibrium type problems arising in Economics, Operations Research, Mathematical Physics, and Transportation. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relaxation approach. This approach is rather flexible and allows one to construct various methods both for single-valued and for multi-valued variational inequalities, including nonlinear constrained problems. The other essential feature of the combined relaxation methods is that they are convergent under very mild assumptions. The book can be viewed as an attempt to discribe the existing combined relaxation methods as a whole.