An alternative approach for a distance inequality associated with the second-order cone and the circular cone

Xin-He Miao Yen-chi Roger Lin Jein-Shan Chen

Optimization and Control mathscidoc:1910.43975

Journal of Inequalities and Applications, 2016, (1), 291, 2016.12
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.
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@inproceedings{xin-he2016an,
  title={An alternative approach for a distance inequality associated with the second-order cone and the circular cone},
  author={Xin-He Miao, Yen-chi Roger Lin, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020230730768255504},
  booktitle={Journal of Inequalities and Applications},
  volume={2016},
  number={1},
  pages={291},
  year={2016},
}
Xin-He Miao, Yen-chi Roger Lin, and Jein-Shan Chen. An alternative approach for a distance inequality associated with the second-order cone and the circular cone. 2016. Vol. 2016. In Journal of Inequalities and Applications. pp.291. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020230730768255504.
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