Combined Relaxation Methods for Variational Inequalities

2001
ISBN: 978-3-540-67999-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 495, 184 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 312 g

Reihe: Lecture Notes in Economics and Mathematical Systems

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.

Zielgruppe

Research

Autoren/Hrsg.

Konnov, Igor

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik

Inhaltsverzeichnis

1. Variational Inequalities with Continuous Mappings.- 1.1 Problem Formulation and Basic Facts.- 1.2 Main Idea of CR Methods.- 1.3 Implementable CR Methods.- 1.4 Modified Rules for Computing Iteration Parameters.- 1.5 CR Method Based on a Frank-Wolfe Type Auxiliary Procedure.- 1.6 CR Method for Variational Inequalities with Nonlinear Constraints.- 2. Variational Inequalities with Multivalued Mappings.- 2.1 Problem Formulation and Basic Facts.- 2.2 CR Method for the Mixed Variational Inequality Problem.- 2.3 CR Method for the Generalized Variational Inequality Problem.- 2.4 CR Method for Multivalued Inclusions.- 2.5 Decomposable CR Method.- 3. Applications and Numerical Experiments.- 3.1 Iterative Methods for Non Strictly Monotone Variational Inequalities.- 3.2 Economic Equilibrium Problems.- 3.3 Numerical Experiments with Test Problems.- 4 Auxiliary Results.- 4.1 Feasible Quasi-Nonexpansive Mappings.- 4.2 Error Bounds for Linearly Constrained Problems.- 4.3 A Relaxation Subgradient Method Without Linesearch.- Bibliographical Notes.- References.