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New Outer Proximal Methods for Solving Variational Inequality Problems

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  • Pham Ngoc Anh

    (Posts and Telecommunications Institute of Technology)

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.

Suggested Citation

  • Pham Ngoc Anh, 2023. "New Outer Proximal Methods for Solving Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 479-501, August.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02202-7
    DOI: 10.1007/s10957-023-02202-7
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    References listed on IDEAS

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    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
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