Article Dans Une Revue Mathematics Année : 2024

About the subgradient method for equilibrium problems

Résumé

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 minmax problems are also stated. These ideas and results deserve to be developed and further refined.

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hal-04629460 , version 1 (26-02-2025)

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  • HAL Id : hal-04629460 , version 1

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Abdellatif Moudafi. About the subgradient method for equilibrium problems. Mathematics , 2024, 12 (13). ⟨hal-04629460⟩
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