No Gap Second-Order Optimality Conditions for Circular Conic Programs

Yue Lu, Jein Shan Chen, Ning Zhang

Research output: Contribution to journalArticle

Abstract

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
Volume40
Issue number10
DOIs
Publication statusPublished - 2019 Jul 27
Externally publishedYes

    Fingerprint

Keywords

  • 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

Cite this