A self-adaptive stochastic subgradient extragradient algorithm for the stochastic pseudomonotone variational inequality problem with application

In this paper, we introduce a stochastic self-adaptive subgradient extragradient approximation algorithm for solving the stochastic pseudomonotone variational inequality problem. The new method uses a variable stepsize generated by the simple computation at each iteration. Contrary to many known algorithms, the resulting algorithm can be easily implemented without prior knowledge of the Lipschitz constant of the mapping, and also without any line search procedure. The convergence and convergence rate of the algorithm are shown. Some numerical examples are given to illustrate the effectiveness of the proposed algorithm. Computation results show that our algorithm has the competitiveness over other related algorithms in the literature. Finally, we apply this algorithm to solve a traffic equilibrium problem.