New projection-type methods for monotone LCP with finite termination

Abstract

In this paper we establish two new projection-type methods for the solution of monotone linear complementarity problem (LCP). The methods are a combination of the extragradient method and the Newton method, in which the active set strategy is used and only one linear system of equations with lower dimension is solved at each iteration. It is shown that under the assumption of monotonicity, these two methods are globally and linearly convergent. Furthermore, under a nondegeneracy condition they have a finite termination property. At last, the methods are extended to solving monotone affine variational inequality problem.