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New Outer Proximal Methods for Solving Variational Inequality Problems

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Abstract

In this paper, we propose a new outer proximal approach for solving the variational inequality problems in the real Euclidean space, where the feasible set is replaced by its polyhedral outer approximation. First, we prove the quasicontractiveness of the outer proximal operator. Second, we apply this property to present two new algorithms and their convergence under strongly monotone and Lipschitz continuous conditions of the cost mapping. Finally, we give some numerical results for the proposed algorithms and comparison with other known methods.

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Acknowledgements

We are very much grateful to the handling Editor and two anonymous referees for their helpful and constructive comments that helped us very much to improve the paper. This research is funded by Posts and Telecommunications Institute of Technology, Hanoi, Vietnam.

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  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Pham Ngoc Anh

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  1. Pham Ngoc Anh
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Correspondence to Pham Ngoc Anh.

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Communicated by Aviv Gibali.

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Anh, P.N. New Outer Proximal Methods for Solving Variational Inequality Problems. J Optim Theory Appl 198, 479–501 (2023). https://doi.org/10.1007/s10957-023-02202-7

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