### Abstract

We consider a regularization method for nonlinear complementarity problems with F being a P_{0}-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 φ_{p} with p > 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 p, for example p ∈ [1.1, 2], usually has better numerical performance, and the generalized FB functions φ_{p} with p ∈ [1.1, 2) can be used as the substitutions for the FB function φ_{2}.

Original language | English |
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Pages (from-to) | 464-479 |

Number of pages | 16 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 220 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2008 Oct 15 |

### Keywords

- Generalized Fischer-Burmeister function
- Nonlinear complementarity problem (NCP)
- P-function
- Semismooth Newton method

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics