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

Author

Listed:
  • Phan Tu Vuong

    (Vienna University of Technology
    HCMC University of Technology and Education)

  • Jean Jacques Strodiot

    (Institute for Computational Science and Technology - HCMC (ICST)
    University of Namur)

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.

Suggested Citation

  • Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0575-0
    DOI: 10.1007/s10898-017-0575-0
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    References listed on IDEAS

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    8. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
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    Cited by:

    1. Phan Tu Vuong & Jean Jacques Strodiot, 2020. "A Dynamical System for Strongly Pseudo-monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 767-784, June.

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