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About the Subgradient Method for Equilibrium Problems

Author

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  • Abdellatif Moudafi

    (L.I.S UMR CNRS 7296, Aix Marseille Université, Campus Universitaire de Saint-Jérôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille, France)

Abstract

Convergence results of the subgradient algorithm for equilibrium problems were mainly obtained using a Lipschitz continuity assumption on the given bifunctions. In this paper, we first provide a complexity result for monotone equilibrium problems without assuming Lipschitz continuity. Moreover, we give a convergence result of the value of the averaged sequence of iterates beyond Lipschitz continuity. Next, we derive a rate convergence in terms of the distance to the solution set relying on a growth condition. Applications to convex minimization and min–max problems are also stated. These ideas and results deserve to be developed and further refined.

Suggested Citation

  • Abdellatif Moudafi, 2024. "About the Subgradient Method for Equilibrium Problems," Mathematics, MDPI, vol. 12(13), pages 1-6, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2081-:d:1427824
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    References listed on IDEAS

    as
    1. A. Nedić & A. Ozdaglar, 2009. "Subgradient Methods for Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 205-228, July.
    2. Alfredo N. Iusem & B. F. Svaiter & Marc Teboulle, 1994. "Entropy-Like Proximal Methods in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 790-814, November.
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