No Gap Second-Order Optimality Conditions for Circular Conic Programs

Yue Lu, Jein Shan Chen*, Ning Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.

Original languageEnglish
Pages (from-to)1113-1135
Number of pages23
JournalNumerical Functional Analysis and Optimization
Issue number10
Publication statusPublished - 2019 Jul 27


  • Circular cone
  • no gap second-order optimality conditions
  • second-order tangent set
  • tangent cone
  • “sigma” term

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization


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