A REGULARIZED OUTER APPROXIMATION METHOD FOR MONOTONE SEMI-INFINITE VARIATIONAL INEQUALITY PROBLEMS

The semi-infinite variational inequality problem (SIVIP) is a variational inequality problem (VIP) whose feasible set is given by infinitely many convex inequalities. To solve SIVIP, we propose an outer approximation method with a regularization technique, which approximately solves a VIP with a finite number of inequality constraints at each iteration. In the algorithm, the regularized gap function is used to specify a criterion for approximate solutions of such VIPs. We establish global convergence of the algorithm by assuming the monotonicity of the problem, Slater's condition, and the existence of a solution. We also report some numerical results to examine the effectiveness of the algorithm.