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

    Résultats de recherche: Contribution à un journal/une revueArticle

    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
    étatPublié - 1 janv. 2016

    Empreinte digitale

    Extragradient Method
    Hilbert spaces
    Equilibrium Problem
    Shrinking
    Projection Method
    Hilbert space
    Projection
    Weak and Strong Convergence
    Line Search
    Monotonicity
    Numerical Experiment
    Sufficient
    Decrease
    Subset
    Experiments
    Class
    Projection method
    Equilibrium problem
    Strategy
    Numerical experiment

    Citer ceci

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    title = "A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces",
    abstract = "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.",
    keywords = "Extragradient methods, Non-monotone equilibrium problems, Shrinking projection methods, Strong convergence, Weak convergence",
    author = "Strodiot, {Jean Jacques} and Vuong, {Phan Tu} and Nguyen, {Thi Thu Van}",
    year = "2016",
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    A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces. / Strodiot, Jean Jacques; Vuong, Phan Tu; Nguyen, Thi Thu Van.

    Dans: Journal of Global Optimization, Vol 64, Numéro 1, 01.01.2016, p. 159-178.

    Résultats de recherche: Contribution à un journal/une revueArticle

    TY - JOUR

    T1 - A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces

    AU - Strodiot, Jean Jacques

    AU - Vuong, Phan Tu

    AU - Nguyen, Thi Thu Van

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    AB - 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.

    KW - Extragradient methods

    KW - Non-monotone equilibrium problems

    KW - Shrinking projection methods

    KW - Strong convergence

    KW - Weak convergence

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