TY - JOUR
T1 - A matrix-splitting method for symmetric affine second-order cone complementarity problems
AU - Hayashi, Shunsuke
AU - Yamaguchi, Takahiro
AU - Yamashita, Nobuo
AU - Fukushima, Masao
N1 - Funding Information:
This research was supported in part by a Grant-in-Aid for Scientific Research (B) from Japan Society for the Promotion of Science.
PY - 2005/3/15
Y1 - 2005/3/15
N2 - 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.
AB - 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.
KW - Complementarity problem
KW - Matrix-splitting method
KW - Second-order cone
KW - Successive overrelaxation method
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U2 - 10.1016/j.cam.2004.05.018
DO - 10.1016/j.cam.2004.05.018
M3 - Article
AN - SCOPUS:10644284037
VL - 175
SP - 335
EP - 353
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 2
ER -