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 setX 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; "; / depending on two parameters "> 0 and > 0. It is worthy to point out that the method will be a feasible point type when " D 0 and an infeasible point type when "> 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; "; /, 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