Smoothan analysis on cone function associated with ellipsoidal cone

Yue Li*, Jein Shan Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


AS an important prototype in closed convex cones, ellipsoidal cone covers several practical instances such as second-order cone, circular cone and elliptic cone. In virtue of a recent study on its decomposition expression, we present a symmetric type of ellipsoidal cone function and show that this vector-valued function inherits some smooth properties from its corresponding scalar function, particularly in continuity, directional differentiability, differentiability and continuous differentiability. We believe that these results will play important roles on further analysis and study about conic programming problems associated with ellipsoidal cone.

Original languageEnglish
Pages (from-to)1327-1347
Number of pages21
JournalJournal of Nonlinear and Convex Analysis
Issue number6
Publication statusPublished - 2020


  • Cone function
  • Ellipsoidal cones
  • Nonsymmetric cones

ASJC Scopus subject areas

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


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