About the Subgradient Method for Equilibrium Problems

Abdellatif Moudafi ()
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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

Mathematics, 2024, vol. 12, issue 13, 1-6

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.

Keywords: subgradient method; equilibrium problem; convex minimization; min–max problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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