An improved prediction–correction method for monotone variational inequalities with separable operators

Abstract

In this paper we study the variational inequality problems with a particular splitting structure, in which the mapping $F$ does not have an explicit form and only its function values can be employed in the numerical methods for solving such problems. Studies and applications of such problems can be found in Fukushima (1992) [3], Glowinski (1984) [4], Glowinski (1989) [5] and Xu (2007) [15]. The paper He et al. (2006) [6] presents an efficient prediction–correction method for such problems. Based on the predictor method in the latter, this paper presents two classes of correction methods which are more convenient to be carried out than that in this reference. Numerical experiments show that the new method is effective.