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September 24, 2025

An inertial-type stochastic self-adaptive algorithm for stochastic pseudomonotone variational inequality problem

Key Points

The proposed algorithm effectively solves the stochastic pseudomonotone variational inequality problem, demonstrating high performance.
Numerical examples illustrate that the new algorithm's performance is competitive with existing methods in variational inequality literature.
The analysis includes convergence rates and oracle complexity, contributing insights into the algorithm's efficiency.
Applications extend to practical problems, such as image restoration, showcasing the algorithm's versatility.

Abstract

In this paper, a new stochastic self-adaptive subgradient extragradient approximation algorithm incorporated inertial technique is proposed to solve the stochastic pseudomonotone variational inequality problem. The convergence, convergence rate and oracle complexity of the algorithm are investigated. A numerical example illustrates the effectiveness of the new algorithm. The numerical results show that our algorithm is competitive with other related algorithms in the literature Yang et al. Variance-based modified backward-forward algorithm with line search for stochastic variational inequality problems and its applications. Asia-Pac J Oper Res. 2020;37(3):2050011 and Wang et al. A self-adaptive stochastic subgradient extragradient algorithm for the stochastic pseudomonotone variational inequality problem with application. Z Angew Math Phys. 2022;73(4):164. Finally, the main results obtained are applied to solve image restoration problem.

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