### Abstract

This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point algorithm is verified to have global and superlinear convergence properties. For the purpose of solving the subproblems efficiently, we introduce a generalized Newton method and show that only one Newton step is eventually needed to obtain a desired approximate solution that approximately satisfies the appropriate criterion under mild conditions. Numerical comparisons are also made with the derivative-free descent method used by Pan and Chen (Optimization 59:1173-1197, 2010), which confirm the theoretical results and the effectiveness of the algorithm.

Original language | English |
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Pages (from-to) | 1037-1063 |

Number of pages | 27 |

Journal | Computational Optimization and Applications |

Volume | 51 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 Apr 1 |

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### Keywords

- Approximation criterion
- Complementarity problem
- Proximal point algorithm
- Second-order cone

### ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Applied Mathematics