## Abstract

In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is globally and Q-linearly convergent to a solution. As an application, the obtained results are used to study the linear second order cone complementarity

problem, with special emphasis on the particular case of positive definite matrices. Moreover, some computational experiments designed to investigate the practical viability of the method are presented.

problem, with special emphasis on the particular case of positive definite matrices. Moreover, some computational experiments designed to investigate the practical viability of the method are presented.

Original language | English |
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Pages (from-to) | 160-181 |

Journal | Linear Algebra and its Applications |

Volume | 513 |

Early online date | 13 Oct 2016 |

DOIs | |

Publication status | Published - 15 Jan 2017 |

## Keywords

- Semi-smooth system
- conic programming
- second order cone
- semi-smooth Newton method