MSSOR-based alternating direction method for symmetric positive-definite linear complementarity problems

Abstract

Finding the solution of linear complementarity problem (LCP) is an important subject in scientific computing, engineering and economic applications. In the literature, many iterative methods have been proposed, especially, when the matrix of the problem is a real positive definite or an H +? matrix. In this paper, we propose a new method using an alternating direction (AD) technique based on a modified symmetric successive overrelaxation (MSSOR) for LCP, assuming that the real matrix of the LCP is symmetric positive definite. This approach is an inner/outer iteration method, in which AD method is used as an outer iteration, and the MSSOR method as an inner one. We provide a detailed proof for the convergence of the proposed method. In addition, numerical results show that the proposed method is feasible and effective.