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Modified Subgradient Extragradient Algorithms with A New Line-Search Rule for Variational Inequalities

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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 mappings. 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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Acknowledgements

The authors thank the editors and reviewers sincerely for their insightful suggestions which improved this work significantly.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Xian-Jun Long & Jing Yang

  2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Xian-Jun Long

  3. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Yeol Je Cho

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  1. Xian-Jun Long
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Correspondence to Xian-Jun Long.

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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

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