New Outer Proximal Methods for Solving Variational Inequality Problems

Pham Ngoc Anh ()
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Pham Ngoc Anh: Posts and Telecommunications Institute of Technology

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 2, No 2, 479-501

Abstract: 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.

Keywords: Quasicontractiveness; Outer approximation; Projection method; Variational inequality problem; Proximal operator; 65K10; 90C25; 49J35; 47J25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02202-7

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