Parabolic Second-Order Directional Differentiability in the Hadamard Sense of the Vector-Valued Functions Associated with Circular Cones

Jinchuan Zhou, Jingyong Tang, Jein Shan Chen

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2 Citations (Scopus)


In this paper, we study the parabolic second-order directional derivative in the Hadamard sense of a vector-valued function associated with circular cone. The vector-valued function comes from applying a given real-valued function to the spectral decomposition associated with circular cone. In particular, we present the exact formula of second-order tangent set of circular cone by using the parabolic second-order directional derivative of projection operator. In addition, we also deal with the relationship of second-order differentiability between the vector-valued function and the given real-valued function. The results in this paper build fundamental bricks to the characterizations of second-order necessary and sufficient conditions for circular cone optimization problems.

Original languageEnglish
Pages (from-to)802-823
Number of pages22
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 2017 Mar 1



  • Circular cone
  • Parabolic second-order derivative
  • Second-order tangent set

ASJC Scopus subject areas

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

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