Abstract
In this paper, we introduce a modified subgradient extragradient algorithm with a new line-search rule for solving pseudomonotone variational inequalities with non-Lipschitz map**s. The new line-search rule is designed by the golden radio \((\sqrt{5}+1)/2\). We prove the strong convergence theorem under some appropriate conditions in real Hilbert spaces. Finally, we give some numerical experiments to illustrate the performances and advantages of the proposed algorithm.
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The authors thank the editors and reviewers sincerely for their insightful suggestions which improved this work significantly.
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Communicated by Anton Abdulbasah Kamil.
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This work was supported by the National Natural Science Foundation of China (11471059), the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0721, cstc2018jcyjAX0119), the Education Committee Project Research Foundation of Chongqing (KJZDK201900801), the Team Building Project for Graduate Tutors in Chongqing (yds223010) and the Project of Chongqing Technology and Business University (KFJJ2022055).
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Long, XJ., Yang, J. & Cho, Y.J. Modified Subgradient Extragradient Algorithms with A New Line-Search Rule for Variational Inequalities. Bull. Malays. Math. Sci. Soc. 46, 140 (2023). https://doi.org/10.1007/s40840-023-01522-1
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DOI: https://doi.org/10.1007/s40840-023-01522-1