The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces

Phan Tu Vuong, Jean Jacques Strodiot

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we introduce a new approach for solving equilibrium problems in Hilbert spaces. First, we transform the equilibrium problem into the problem of finding a zero of a sum of two maximal monotone operators. Then, we solve the resulting problem using the Glowinski–Le Tallec splitting method and we obtain a linear rate of convergence depending on two parameters. In particular, we enlarge significantly the range of these parameters given rise to the convergence. We prove that the sequence generated by the new method converges to a global solution of the considered equilibrium problem. Finally, numerical tests are displayed to show the efficiency of the new approach.

    Original languageEnglish
    Pages (from-to)477–495
    Number of pages19
    JournalJournal of Global Optimization
    Volume70
    Issue number2
    DOIs
    Publication statusPublished - 9 Oct 2017

    Keywords

    • Equilibrium problem
    • Global convergence
    • Glowinski–Le Tallec splitting method
    • Maximal monotone operator
    • Nash equilibrium

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