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

被引：6

作者：

Zhou, Jinchuan ^{[1
]}

Tang, Jingyong ^{[2
]}

Chen, Jein-Shan ^{[3
]}

机构：

[1] Shandong Univ Technol, Sch Sci, Dept Math, Zibo 255049, Shandong, Peoples R China

[2] Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China

[3] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2017年 / 172卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Parabolic second-order derivative; Circular cone; Second-order tangent set; CONVEX-FUNCTIONS; SOC-MONOTONE; DERIVATIVES; SMOOTH;

D O I：

10.1007/s10957-016-0935-9

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：802 / 823

页数：22

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