Algorithms for Finding Minimum-Norm Solutions of Quasimonotone Variational Inequalities

doi:10.1007/s40305-025-00606-y

Abstract

Abstract: This paper introduces two novel self-adaptive extragradient projection methods for solving variational inequalities involving Lipschitz continuous and quasimonotone mappings in real Hilbert spaces. Our proposed methods incorporate an inertial step into a single projection framework, leveraging the potential advantages of inertial techniques to accelerate convergence. We rigorously establish strong convergence theorems for the proposed algorithms, providing theoretical guarantees for their convergence behavior under appropriate assumptions. Furthermore, to evaluate the practical efficacy of our methods, we present comprehensive numerical experiments and comparisons.

Key words: Variational inequality, Quasimonotone mapping, Lipschitz continuity, Inertial technique, Strong convergence

CLC Number:

47H09·47J20·65K15·90C25

Duong Viet Thong, Xiao-Huan Li, Pham Thi Hong Tham, Nguyen Hai Duong. Algorithms for Finding Minimum-Norm Solutions of Quasimonotone Variational Inequalities[J]. Journal of the Operations Research Society of China, 2026, 14(3): 1061-1087.

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URL: https://www.jorsc.shu.edu.cn/EN/10.1007/s40305-025-00606-y

https://www.jorsc.shu.edu.cn/EN/Y2026/V14/I3/1061

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Algorithms for Finding Minimum-Norm Solutions of Quasimonotone Variational Inequalities

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