Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints

In this paper, we introduce the modified Mann-like subgradient-like extragradient implicit rules with linear-search process for finding a common solution of a system of generalized equilibrium problems, a pseudomonotone variational inequality problem and a fixed-point problem of an asymptotically no...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 2; pp. 2961 - 2994
Main Authors Ceng, Lu-Chuan, Zhu, Li-Jun, Yin, Tzu-Chien
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
convergence
fixed point
subgradient extragradient method
system of generalized equilibrium problems
variational inequality
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Summary:In this paper, we introduce the modified Mann-like subgradient-like extragradient implicit rules with linear-search process for finding a common solution of a system of generalized equilibrium problems, a pseudomonotone variational inequality problem and a fixed-point problem of an asymptotically nonexpansive mapping in a real Hilbert space. The proposed algorithms are based on the subgradient extragradient rule with linear-search process, Mann implicit iteration approach, and hybrid deepest-descent technique. Under mild restrictions, we demonstrate the strong convergence of the proposed algorithms to a common solution of the investigated problems, which is a unique solution of a certain hierarchical variational inequality defined on their common solution set.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023154