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

Jinchuan Zhou, Jingyong Tang, Jein Shan Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)2115-2133
Number of pages19
Issue number12
Publication statusPublished - 2016 Dec 1


  • KKT system
  • Positive semidefinite matrix cone
  • normal cone
  • projection
  • second-order cone
  • tangent cone

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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