A VARIANCE-BASED PROXIMAL BACKWARD-FORWARD ALGORITHM WITH LINE SEARCH FOR STOCHASTIC MIXED VARIATIONAL INEQUALITIES

摘要

In this paper, we introduce a new variance-based proximal backward-forward algorithm with line search for stochastic mixed variational inequalities, which only needs to compute one proximal operator per iteration. Particularly, the proposed algorithm only requires the mapping F to be g-pseudomonotone and does not need to know any information of the Lipschitz constant of the mapping while other similar methods require the monotonicity and the information of the Lipschitz constant. Moreover, we analyse some properties of the proposed algorithm related to the asymptotic convergence, the linear convergence rate with finite computational budget and the optimal oracle complexity under some moderate conditions. Finally, some numerical experiments are given to show the efficiency and advantages of the algorithm introduced in this paper.