### Abstract

We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it - for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p ∈ (1, 2] has better numerical performance than the one with p > 2.

Original language | English |
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Pages (from-to) | 3739-3758 |

Number of pages | 20 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 72 |

Issue number | 9-10 |

DOIs | |

Publication status | Published - 2010 May 1 |

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### Keywords

- Convergence rate
- Mixed complementarity problem
- Smoothing approximation
- The generalized FB function

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*72*(9-10), 3739-3758. https://doi.org/10.1016/j.na.2010.01.012