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

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    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
    Volume172
    Issue number3
    DOIs
    Publication statusPublished - 2017 Mar 1

    Keywords

    • 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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