Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2003-008 (June 30, 2003)

A Matrix Splitting Method for Symmetric Affine Second-Order Cone Complementarity Problems
by Shunsuke Hayashi, Takahiro Yamaguchi, Nobuo Yamashita and Masao Fukushima

PostScript File

The affine Second-Order Cone Complementarity Problem (SOCCP) is a wide class of problems that contains the Linear Complementarity Problem (LCP) as a special case. The purpose of this paper is to propose an iterative method for the symmetric affine SOCCP that is based on the idea of matrix splitting. Matrix splitting methods have originally been developed for the solution of the system of linear equations and have subsequently been extended to the linear complementarity problem (LCP) and the affine variational inequality problem. In this paper, we first give conditions under which the matrix splitting method converges to a solution of the affine SOCCP. We then present, as a particular realization of the matrix splitting method, the block successive overrelaxation (SOR) method for the affine SOCCP involving a positive definite matrix, and propose an efficient method for solving subproblems. Finally, we report some numerical results with the proposed algorithm, where promising results are obtained especially for problems with sparse matrices.