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Open AccessArticle
About the Subgradient Method for Equilibrium Problems
by
Abdellatif Moudafi
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, 12(13), 2081; https://doi.org/10.3390/math12132081 (registering DOI)
Submission received: 12 June 2024
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Revised: 26 June 2024
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Accepted: 1 July 2024
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Published: 2 July 2024
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.
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MDPI and ACS Style
Moudafi, A.
About the Subgradient Method for Equilibrium Problems. Mathematics 2024, 12, 2081.
https://doi.org/10.3390/math12132081
AMA Style
Moudafi A.
About the Subgradient Method for Equilibrium Problems. Mathematics. 2024; 12(13):2081.
https://doi.org/10.3390/math12132081
Chicago/Turabian Style
Moudafi, Abdellatif.
2024. "About the Subgradient Method for Equilibrium Problems" Mathematics 12, no. 13: 2081.
https://doi.org/10.3390/math12132081
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