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

Jinchuan Zhou, Jingyong Tang and Jein-Shan Chen ()
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Jinchuan Zhou: Shandong University of Technology
Jingyong Tang: Xinyang Normal University
Jein-Shan Chen: National Taiwan Normal University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 3, No 5, 802-823

Abstract: 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.

Keywords: Parabolic second-order derivative; Circular cone; Second-order tangent set; 90C30; 49J52; 46G05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0935-9

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