### Abstract

Let K^{n} be the Lorentz/second-order cone in IR^{n}. For any function f from IR to IR, one can define a corresponding vector-valued function f^{soc} (x) on IR^{n} by applying f to the spectral values of the spectral decomposition of x ∈ IR^{n} with respect to K^{n}. It was shown by J.-S. Chen, X. Chen and P. Tseng in [5] that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as semismoothness. In this note, we further show that the Holder continuity of this vector-valued function is also inherited from f. Such property will be useful in designing solution methods for second-order cone programming and second-order cone complementarity problem.

Original language | English |
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Pages (from-to) | 135-141 |

Number of pages | 7 |

Journal | Pacific Journal of Optimization |

Volume | 8 |

Issue number | 1 |

Publication status | Published - 2012 Jan 1 |

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### Keywords

- Hölder continuity
- Second-order cone

### ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Applied Mathematics