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Combined Relaxation Methods for Variational Inequalities

  • Book
  • © 2001

Overview

Authors:
  1. Igor Konnov

    1. Department of Applied Mathematics, Kazan University, Kazan, Russia

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XI
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  2. Notation and Convention

    • Igor Konnov
    Pages 1-2

  3. Variational Inequalities with Continuous Mappings

    • Igor Konnov
    Pages 3-56

  4. Variational Inequalities with Multivalued Mappings

    • Igor Konnov
    Pages 57-107

  5. Applications and Numerical Experiments

    • Igor Konnov
    Pages 109-141

  6. Auxiliary Results

    • Igor Konnov
    Pages 143-160

  7. Back Matter

    Pages 161-184
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Applied Mathematics, Kazan University, Kazan, Russia

    Igor Konnov

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