A descent method for a reformulation of the second-order cone complementarity problem

Analogous to the nonlinear complementarity problem (NCP) and the semidefinite complementarity problem (SDCP), a popular approach to solving the secondorder cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over IR. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the Fischer-Burmeister merit function associated with second-order cone [4], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FischerBurmeister merit function approach [4]. The comparison results indicate that, if a scaling strategy is imposed on the test problem, the descent method proposed is comparable with the merit function approach in the CPU time for solving test problems although the former may require more function evaluations.