A reconsideration on convergence of the extra-gradient method for solving quasimonotone variational inequalities

In this paper, we continue to investigate convergence of the extra-gradient method for solving quasimonotone variational inequalities in Hilbert spaces. Under some suitable conditions, we prove that the iterative sequence generated by the extra-gradient method converges weakly to a solution of quasi...

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Bibliographic Details
Published inOptimization Vol. 74; no. 8; pp. 1957 - 1968
Main Authors Zhu, Li-Jun, Yin, Tzu-Chien
Format Journal Article
LanguageEnglish
Published Taylor & Francis 11.06.2025
Subjects
extra-gradient method
quasimonotone operator
Variational inequality
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Summary:In this paper, we continue to investigate convergence of the extra-gradient method for solving quasimonotone variational inequalities in Hilbert spaces. Under some suitable conditions, we prove that the iterative sequence generated by the extra-gradient method converges weakly to a solution of quasimonotone variational inequalities. Our result corrects and improves the main result in Salahuddin [The extra-gradient method for quasimonotone variational inequalities. Optimization. 2022;71:2519-2528].
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2341941