A regularized smoothing Newton method for solving SOCCPs based on a new smoothing C-function

In this paper, an SOC complementarity function is constructed. Based on this function, a regularized smoothing Newton method is proposed for solving monotone second-order cone complementarity problems (denoted by SOCCPs). The proposed algorithm is proved to be globally and quadratically convergent under mild conditions. Unlike some existing smoothing Newton-type methods, we take the regularization parameter the same as the smoothing parameter μ and treat the parameter μ as independent variables in our algorithm. Some numerical results are reported and indicate that the proposed method is quite effective.