A Matrix Splitting Method For Second-order Cone Complementarity Problems And Second-order Cone Programming

The second order cone complementarity problem(SOCCP) is a wide range 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 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 that subsequently been extended to the LCP and the affine variational inequality problem. In this paper, we first give the framework of matrix splitting method and its convergence analysis, we then present, as a particular realization of the matrix-splitting method, the block succes-sive overrelaxation(SOR) method for the SOCCP, and propose an efficient method for solving subproblems, then report some numerical results with the proposed algorithm. Finally, as an application to the matrix-splitting method for SOCCP, we consider the second-order cone programming(SOCP) problem, and then give an algorithm based on line search method plus some related numerical results.