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Nong Thu Trang, Do Duy Thanh, Hoang Thi Cam Thach, Pham Ngoc Anh, A new approximation approach to variational inequality problems

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DOI: 10.23952/asvao.8.2026.3.06
Volume 8, Issue 3, 1 December 2026, Pages 373-392

 

Abstract. In this paper, we develop a new approximation approach for solving variational inequalities in real Hilbert spaces. The main novelty lies in the construction of two solution mappings, for which strong quasi-nonexpansiveness is established. These mappings are then incorporated into a relaxed projection scheme for solving a class of bilevel variational inequalities. Under pseudomonotonicity assumptions on the associated cost mappings, we establish the strong convergence of the proposed iterative algorithms to a solution of the bilevel variational inequalities. Furthermore, several numerical experiments are conducted to illustrate the computational performance and practical effectiveness of the proposed approach.

 

How to Cite this Article:
N.T. Trang, D.D. Thanh, H.T.C. Thach, P.N. Anh, A new approximation approach to variational inequality problems, Appl. Set-Valued Anal. Optim. 8 (2026), 373-392.