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.