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Regularization projection method for solving bilevel variational inequality problem

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Abstract

In this paper, we propose a regularization projection method for solving a bilevel variational inequality problem in a Hilbert space. We first describe how to incorporate the regularization technique and the modified subgradient extragradient—like method, and then establish the strong convergence of the resulting algorithm under some suitable conditions. The new algorithm requires to compute only one projection on feasible set, and it can be easily implemented without the prior knowledge of Lipschitz and strongly monotone constants of operators. The obtained results in the paper improve and extend some related results in the literature. Several numerical results are reported to illustrate the computational performance of the proposed algorithm.

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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. The first author 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. Aix-Marseille Université, LIS UMR CNRS 7020, Marseille, France

    Abdellatif Moudafi

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  1. Dang Van Hieu
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Correspondence to Abdellatif Moudafi.

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Van Hieu, D., Moudafi, A. Regularization projection method for solving bilevel variational inequality problem. Optim Lett 15, 205–229 (2021). https://doi.org/10.1007/s11590-020-01580-5

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