Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509616 | Journal of Computational and Applied Mathematics | 2005 | 19 Pages |
Abstract
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 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Shunsuke Hayashi, Takahiro Yamaguchi, Nobuo Yamashita, Masao Fukushima,