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

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

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish
    Pages (from-to)373-397
    Number of pages25
    JournalJournal of Global Optimization
    Issue number2
    Publication statusPublished - 1 Jun 2013


    • Generalized Nash equilibrium problems
    • Hybrid extragradient methods
    • Quasi-equilibrium problems
    • Quasi-variational inequalities


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