### Abstract

In the paper [J.-S. Chen, S. Pan, A family of NCP-functions and a descent method for the nonlinear complementarity problem, Computational Optimization and Applications, 40 (2008) 389-404], the authors proposed a derivative-free descent algorithm for nonlinear complementarity problems (NCPs) by the generalized Fischer-Burmeister merit function: ψ_{p} (a, b) = frac(1, 2) [{norm of matrix} (a, b) {norm of matrix}_{p} - (a + b)]^{2}, and observed that the choice of the parameter p has a great influence on the numerical performance of the algorithm. In this paper, we analyze the phenomenon theoretically for a derivative-free descent algorithm which is based on a penalized form of ψ_{p} and uses a different direction from that of Chen and Pan. More specifically, we show that the algorithm proposed is globally convergent and has a locally R-linear convergence rate, and furthermore, its convergence rate will become worse when the parameter p decreases. Numerical results are also reported for the test problems from MCPLIB, which further verify the theoretical results obtained.

Original language | English |
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Pages (from-to) | 455-471 |

Number of pages | 17 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 232 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 Oct 15 |

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### Keywords

- Convergence rate
- Global error bound
- Merit function
- NCP-function
- Nonlinear complementarity problem

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational and Applied Mathematics*,

*232*(2), 455-471. https://doi.org/10.1016/j.cam.2009.06.022