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Combined Relaxation Methods for Variational Inequalities

  • Igor Konnov

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 495)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Igor Konnov
    Pages 1-2
  3. Igor Konnov
    Pages 109-141
  4. Igor Konnov
    Pages 143-160
  5. Back Matter
    Pages 161-184

About this book

Introduction

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.

Keywords

Combined Relaxation Methods Generalized Monotone Mapppings Ungleichungssysteme Variational Inequalities Variationsgleichungen operations research

Authors and affiliations

  • Igor Konnov
    • 1
  1. 1.Department of Applied MathematicsKazan UniversityKazanRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-56886-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67999-8
  • Online ISBN 978-3-642-56886-2
  • Series Print ISSN 0075-8442
  • Series Online ISSN 2196-9957
  • Buy this book on publisher's site
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