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Strong convergence of subgradient extragradient method with regularization for solving variational inequalities

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Abstract

The paper concerns with the two numerical methods for approximating solutions of a monotone and Lipschitz variational inequality problem in a Hilbert space. We here describe how to incorporate regularization terms in the projection method, and then establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. The new methods work in both cases of with or without knowing previously the Lipschitz constant of cost operator. Using the regularization aims mainly to obtain the strong convergence of the methods which is different to the known hybrid projection or viscosity-type methods. The effectiveness of the new methods over existing ones is also illustrated by several numerical experiments.

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Acknowledgements

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. This paper is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2020.06.

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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

    Dang Van Hieu

  2. Department of Mathematics, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Pham Ky Anh

  3. TIMAS, Thang Long University, Hanoi, Vietnam

    Le Dung Muu

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  1. Dang Van Hieu
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  2. Pham Ky Anh
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  3. Le Dung Muu
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Correspondence to Dang Van Hieu.

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Van Hieu, D., Anh, P.K. & Muu, L.D. Strong convergence of subgradient extragradient method with regularization for solving variational inequalities. Optim Eng 22, 2575–2602 (2021). https://doi.org/10.1007/s11081-020-09540-9

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  • DOI: https://doi.org/10.1007/s11081-020-09540-9

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