Using schur complement theorem to prove convexity of some SOC-functions

Jein Shan Chen, Tsun Ko Liao, Shaohua Pan

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper, we provide an important application of the Schur Complement Theorem in establishing convexity of some functions associated with second-order cones (SOCs), called SOC-trace functions. As illustrated in the paper, these functions play a key role in the development of penalty and barrier functions methods for second-order cone programs, and establishment of some important inequalities associated with SOCs.

Original languageEnglish
Pages (from-to)421-431
Number of pages11
JournalJournal of Nonlinear and Convex Analysis
Issue number3
Publication statusPublished - 2012 Jul


  • Convexity
  • Positive semidefiniteness
  • Second-order cone
  • SOC-functions

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics


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