An analytic center cutting plane method for solving semi-infinite variational inequality problems

We study a variational inequality problem VI(X,F) with X being defined by infinitely many inequality constraints and F being a pseudomonotone function. It is shown that such problem can be reduced to a problem of finding a feasible point in a convex set defined by infinitely many constraints. An analytic center based cutting plane algorithm is proposed for solving the reduced problem. Under proper assumptions, the proposed algorithm finds an epsilon-optimal solution in O*(n(2)/rho(2)) iterations, where O*(.) represents the leading order, n is the dimension of X, epsilon is a user-specified tolerance, and rho is the radius of a ball contained in the epsilon-solution set of VI(X,F).