A feasible descent algorithm for solving variational inequality problems

Abstract

In this paper, for solving variational inequality problems (VIPs) we propose a feasible descent algorithm via minimizing the regularized gap function of Fukushima. Under the condition that the underlying mapping of VIP is strongly monotone, the algorithm is globally convergent for any regularized parameter, which is nice because it bypasses the necessity of knowing the modulus of strong monotonicity, a knowledge that is requested by other similar algorithms. Some preliminary computational results show the efficiency of the proposed method.