Combined Relaxation Methods for Variational Inequalities

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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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.

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

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

  Igor Konnov

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