An inexact smoothing method for SOCCPs based on a one-parametric class of smoothing function

In this paper, we introduce a one-parametric class of smoothing functions which contains the Fischer–Burmeister smoothing function as special case. Based on this class of smoothing functions, an inexact smoothing method for solving second-order cone complementarity problems (SOCCPs) is proposed. In each iteration the corresponding linear system is solved only approximately. Under mild assumptions, it is proved that the proposed method has global convergence and local superlinear convergence properties. Preliminary numerical results indicate that the method is effective for large-scale problems.