Iterative Algorithms for Equilibrium Problems

We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances...

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Bibliographic Details
Published inOptimization Vol. 52; no. 3; pp. 301 - 316
Main Authors Iusem, Alfredo N., Sosa, Wilfredo
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2003
Subjects
Convex Feasibility Problems
Equilibrium Problems
Mathematics Subject Classification 2000: 49m37
Projection Methods
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Summary:We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets, but with additional structure, so that projection algorithms for convex feasibility can be modified in order to improve their convergence properties, mainly achieving global convergence without either compactness or coercivity assumptions. We present a sequential projections algorithm with an approximately most violated constraint control strategy, and two variants where exact orthogonal projections are replaced by approximate ones, using separating hyperplanes generated by subgradients. We include full convergence analysis of these algorithms.
ISSN:0233-1934
1029-4945
DOI:10.1080/0233193031000120039