A regularization semismooth Newton method based on the generalized Fischer–Burmeister function for P0P0-NCPs

We consider a regularization method for nonlinear complementarity problems with FF being a P0P0-function which replaces the original problem with a sequence of the regularized complementarity problems. In this paper, this sequence of regularized complementarity problems are solved approximately by applying the generalized Newton method for an equivalent augmented system of equations, constructed by the generalized Fischer–Burmeister (FB) NCP-functions φpφp with p>1p>1. We test the performance of the regularization semismooth Newton method based on the family of NCP-functions through solving all test problems from MCPLIB. Numerical experiments indicate that the method associated with a smaller pp, for example p∈[1.1,2]p∈[1.1,2], usually has better numerical performance, and the generalized FB functions φpφp with p∈[1.1,2)p∈[1.1,2) can be used as the substitutions for the FB function φ2φ2.