A regularized smoothing Newton method for solving the symmetric cone complementarity problem

The symmetric cone complementarity problem (denoted by SCCP) is a class of equilibrium optimization problems, and it contains the standard linear/nonlinear complementarity problem (LCP/NCP), the second‐order cone complementarity problem (SOCCP) and the semidefinite complementarity problem (SDCP) as special cases. In this paper, we present a regularized smoothing Newton algorithm for SCCP by making use of Euclidean Jordan algebraic technique. Under suitable conditions, we obtain global convergence and local quadratic convergence of the proposed algorithm. Some numerical results are reported in this paper, which confirm the good theoretical properties of the proposed algorithm.