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Further relationship between second-order cone and positive semidefinite matrix cone

Jinchuan Zhou Jingyong Tang Jein-Shan Chen

Optimization and Control mathscidoc:1910.43941

Optimization, 65, (12), 2115-2133, 2016.12
It is well known that second-order cone (SOC) programming can be regarded as a special case of positive semidefinite programming using the arrow matrix. This paper further studies the relationship between SOCs and positive semidefinite matrix cones. In particular, we explore the relationship to expressions regarding distance, projection, tangent cone, normal cone and the KKT system. Understanding these relationships will help us see the connection and difference between the SOC and its PSD reformulation more clearly.
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@inproceedings{jinchuan2016further,
  title={Further relationship between second-order cone and positive semidefinite matrix cone},
  author={Jinchuan Zhou, Jingyong Tang, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225626530381470},
  booktitle={Optimization},
  volume={65},
  number={12},
  pages={2115-2133},
  year={2016},
}
Jinchuan Zhou, Jingyong Tang, and Jein-Shan Chen. Further relationship between second-order cone and positive semidefinite matrix cone. 2016. Vol. 65. In Optimization. pp.2115-2133. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225626530381470.
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