On the convergence of a matrix splitting algorithm for the symmetric linear complementarity problem

We consider a matrix splitting algorithm for the linear complementarity problem where the matrix is symmetric positive semi-definite. We show that if the splitting is regular, then the iterates generated by the algorithm are well defined and converge to a solution. This result resolves in the affirmative a long standing question about the convergence of the point SOR method for solving this problem. We also extend this result to related iterative methods. As direct consequences, we obtain convergence of the methods of, respectively, Aganagic, Cottle et al., Mangasarian, Pang, and others, without making any additional assumption on the problem.