A Combined Feasible-Infeasible Point Continuation Method for Strongly Monotone Variational Inequality Problems

Abstract

In this paper, we discuss the variational inequality problems VIP(X, F), where F is a strongly monotone function and the convex feasible set X is described by some inequaliy constraints. We present a continuation method for VIP(X, F), which solves a sequence of perturbed variational inequality problems PVIP(X, F, ε, μ) depending on two parameters ε ≥ 0 and μ>0. It is worthy to point out that the method will be a feasible point type when ε=0 and an infeasible point type when ε>0, i.e., it is a combined feasible–infeasible point (CFIFP for short) method. We analyse the existence, uniqueness and continuity of the solution to PVIP(X, F, ε, μ), and prove that any sequence generated by this method converges to the unique solution of VIP(X, F). Moreover, some numerical results of the algorithm are reported which show the algorithm is effective.