PROXIMAL-LIKE SUBGRADIENT METHODS FOR SOLVING MULTI-VALUED VARIATIONAL INEQUALITIES

Abstract

In this paper, we propose and analyze the convergence of a new algorithm for solving monotone and Lipschitz continuous multi-valued variational inequalities by using proximal operator. By choosing suitable parameters of proximal steps and of subgradient stepsizes, we show that the convergence of the algorithm does not require the prior knowledge of Lipschitz continuous constant of cost operator.