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

Author

Listed:
  • Jinchuan Zhou

    (Shandong University of Technology)

  • Jingyong Tang

    (Xinyang Normal University)

  • Jein-Shan Chen

    (National Taiwan Normal University)

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.

Suggested Citation

  • Jinchuan Zhou & Jingyong Tang & Jein-Shan Chen, 2017. "Parabolic Second-Order Directional Differentiability in the Hadamard Sense of the Vector-Valued Functions Associated with Circular Cones," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 802-823, March.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-0935-9
    DOI: 10.1007/s10957-016-0935-9
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    References listed on IDEAS

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    1. C. Gutiérrez & B. Jiménez & V. Novo, 2009. "New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 85-106, July.
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    Cited by:

    1. Jingyong Tang & Jinchuan Zhou, 2020. "Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones," Annals of Operations Research, Springer, vol. 295(2), pages 787-808, December.

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