Some New Conditions for Solving Variational Inequalities Without Monotonicity

Duong Viet Thong ()
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Duong Viet Thong: National Economics University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 8, 20 pages

Abstract: Abstract This work aims to provide some new conditions for approximating a solution of the variational inequality problem without monotonicity in a real Hilbert space. We obtain a weak convergence result of the proposed method that hasn’t been investigated before in the literature. Our results improve and extend the relaxed inertial Tseng extragradient method for the class of nonlinear mappings without using any monotonicity.

Keywords: Non-monotone mapping; relaxed inertial Tseng’s extragradient method; variational inequality; weak convergence; 65Y05; 65K15; 68W10; 47H09; 47J25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02718-0

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