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A strong convergence theorem for Tseng’s extragradient method for solving variational inequality problems

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Abstract

In this paper, we introduce a new algorithm for solving variational inequality problems with monotone and Lipschitz-continuous mappings in real Hilbert spaces. Our algorithm requires only to compute one projection onto the feasible set per iteration. We prove under certain mild assumptions, a strong convergence theorem for the proposed algorithm to a solution of a variational inequality problem. Finally, we give some numerical experiments illustrating the performance of the proposed algorithm for variational inequality problems.

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Acknowledgements

The authors would like to two anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper. This paper was completed when the first two authors were visiting the Vietnam Institute for Advance Study in Mathematics (VIASM) and they thank the VIASM for financial support and hospitality and the second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No.101.01-2017.08.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, University of Transport and Communications, Hanoi City, Vietnam

    Nguyen The Vinh

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

    Yeol Je Cho

  4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yeol Je Cho

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  1. Duong Viet Thong
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  2. Nguyen The Vinh
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  3. Yeol Je Cho
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Correspondence to Yeol Je Cho.

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Thong, D.V., Vinh, N.T. & Cho, Y.J. A strong convergence theorem for Tseng’s extragradient method for solving variational inequality problems. Optim Lett 14, 1157–1175 (2020). https://doi.org/10.1007/s11590-019-01391-3

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