Two-stage parallel iterative methods for the symmetric linear complementarity problem

In this paper, we propose a two-stage parallel iterative method for solving the symmetric linear complementarity problem. When implemented in a parallel computing environment, the method decomposes the problem into subproblems which are solved by certain iterative procedures concurrently on separate processors. Convergence of the overall method is established under some mild assumptions on how the inner iterations are terminated. Applications of the proposed method to solve strictly convex quadratic programs are discused and numerical results on both a sequential computer (IBM 4381) and a super-computer (CRAYX-MP/24) are reported.This research was based on work supported by the National Science Foundation under grant ECS-8407240 and by a 1986 University Research and Development grant from Cray Research Inc.