The numerical study of a regularized smoothing Newton method for solving P 0-NCP based on the generalized smoothing Fischer‐Burmeister function

The nonlinear complementarity problems (denoted by NCPs) usually are reformulated as the solution of a nonsmooth system of equations. In this paper, we will present a regularized smoothing Newton method for solving nonlinear complementarity problems with P 0‐function (P 0‐NCPs) based on the generalized smoothing Fischer–Burmeister NCP‐function φ p (μ, a, b) with p >1, where μ is smoothing parameter. Without requiring strict complementarity assumption at the P 0‐NCPs solution, the proposed algorithm is proved to be globally and superlinearly convergent under suitable assumptions. Furthermore, the algorithm is locally quadratic convergent under mild conditions. Numerical experiments indicate that the proposed method is quite effective. In addition, in this paper, the regularization parameter e in our algorithm is viewed as an independent variable, hence, our algorithm seems to be simpler and more easily implemented compared to many existing literatures.