A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems

Jean-Jacques Strodiot, Thi Thu Van Nguyen, Van Hien Nguyen

    Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs

    Résumé

    Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.

    langue originaleAnglais
    Pages (de - à)373-397
    Nombre de pages25
    journalJournal of Global Optimization
    Volume56
    Numéro de publication2
    Les DOIs
    Etat de la publicationPublié - 1 juin 2013

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