### Abstract

Analogous to the nonlinear complementarity problem and the semi-definite complementarity problem, a popular approach to solving the second-order cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over R^{n}. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the Fischer-Burmeister merit function (FBMF) associated with second-order cone [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FBMF approach [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327]. The comparison results indicate that, if a scaling strategy is imposed on the test problem, the descent method proposed is comparable with the merit function approach in the CPU time for solving test problems although the former may require more function evaluations.

Original language | English |
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Pages (from-to) | 547-558 |

Number of pages | 12 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 213 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Apr 1 |

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### Keywords

- Complementarity
- Descent method
- Merit function
- Second-order cone

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics