## 摘要

It is well known that the second-order cone and the circular cone have many analogous properties. In particular, there exists an important distance inequality associated with the second-order cone and the circular cone. The inequality indicates that the distances of arbitrary points to the second-order cone and the circular cone are equivalent, which is crucial in analyzing the tangent cone and normal cone for the circular cone. In this paper, we provide an alternative approach to achieve the aforementioned inequality. Although the proof is a bit longer than the existing one, the new approach offers a way to clarify when the equality holds. Such a clarification is helpful for further study of the relationship between the second-order cone programming problems and the circular cone programming problems.

原文 | 英語 |
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文章編號 | 291 |

期刊 | Journal of Inequalities and Applications |

卷 | 2016 |

發行號 | 1 |

DOIs | |

出版狀態 | 已發佈 - 2016 12月 1 |

## ASJC Scopus subject areas

- 分析
- 離散數學和組合
- 應用數學