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Versions of the Subgradient Extragradient Method for Pseudomonotone Variational Inequalities

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Abstract

We develop versions of the subgradient extragradient method for variational inequalities in Hilbert spaces and establish sufficient conditions for their convergence. First we prove a sufficient condition for a weak convergence of a recent existing algorithm under relaxed assumptions. Then, we propose two other algorithms. Both weak and strong convergence of the considered algorithms are studied. Under additional strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a \(Q\)-linear convergence rate of these algorithms. Our results improve some recent contributions in the literature. Illustrative numerical experiments are also provided by the end of the paper.

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Acknowledgements

The first author is supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under the grant number 101.01-2020.23. A significant part of the paper was completed during a scientific stay of the authors at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose support and hospitality are gratefully appreciated. The third named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2020.09. The authors are very thankful to the Editor and the two anonymous Reviewers for their valuable remarks and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, International University, Vietnam National University-Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

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

    Duong Viet Thong

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

    Nguyen The Vinh

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  1. Phan Quoc Khanh
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  2. Duong Viet Thong
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  3. Nguyen The Vinh
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Correspondence to Duong Viet Thong.

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Khanh, P.Q., Thong, D.V. & Vinh, N.T. Versions of the Subgradient Extragradient Method for Pseudomonotone Variational Inequalities. Acta Appl Math 170, 319–345 (2020). https://doi.org/10.1007/s10440-020-00335-9

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