Parabolic Second-Order Directional Differentiability in the Hadamard Sense of the Vector-Valued Functions Associated with Circular Cones |
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Authors: | Jinchuan Zhou Jingyong Tang Jein-Shan Chen |
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Institution: | 1.Department of Mathematics, School of Science,Shandong University of Technology,Zibo,People’s Republic of China;2.College of Mathematics and Information Science,Xinyang Normal University,Xinyang,People’s Republic of China;3.Department of Mathematics,National Taiwan Normal University,Taipei,Taiwan |
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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. |
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