More results on the convergence of iterative methods for the symmetric linear complementarity problem

Abstract

In an earlier paper, the author has given some necessary and sufficient conditions for the convergence of iterative methods for solving the linear complementarity problem. These conditions may be viewed as global in the sense that they apply to the methods regardless of the constant vector in the linear complementarity problem. More precisely, the conditions characterize a certain class of matrices for which the iterative methods will converge, in a certain sense, to a solution of the linear complementarity problem for all constant vectors. In this paper, we improve on our previous results and establish necessary and sufficient conditions for the convergence of iterative methods for solving each individual linear complementarity problem with a fixed constant vector. Unlike the earlier paper, our present analysis applies only to the symmetric linear complementarity problem. Various applications to a strictly convex quadratic program are also given.