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

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.