Inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and fixed point problems in Hilbert spaces

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm con...

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Bibliographic Details
Published inOptimization Vol. 73; no. 5; pp. 1329 - 1354
Main Authors Xie, Zhongbing, Cai, Gang, Tan, Bing
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.05.2024
Taylor & Francis LLC
Subjects
Convergence
Equilibrium problem
fixed point
Hilbert space
Iterative algorithms
pseudomonotone bifunction
strong convergence
subgradient extragradient method
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Summary:This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2157677