A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces

Jean Jacques Strodiot, Phan Tu Vuong, Thi Thu Van Nguyen

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    Résumé

    A new class of extragradient-type methods is introduced for solving an equilibrium problem in a real Hilbert space without any monotonicity assumption on the equilibrium function. The strategy is to replace the second projection step in the classical extragradient method by a projection onto shrinking convex subsets of the feasible set. Furthermore, to ensure a sufficient decrease on the equilibrium function, a general Armijo-type condition is imposed. This condition is shown to be satisfied for four different linesearches used in the literature. Then, the weak and strong convergence of the resulting algorithms is obtained under non-monotonicity assumptions. Finally, some numerical experiments are reported.

    langue originaleAnglais
    Pages (de - à)159-178
    Nombre de pages20
    journalJournal of Global Optimization
    Volume64
    Numéro de publication1
    Les DOIs
    Etat de la publicationPublié - 1 janv. 2016

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