Variational Analysis of the Ky Fan k-norm

doi:10.1007/s11228-016-0378-3

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	Variational Analysis of the Ky Fan k-norm
	Ding, Chao
	2017-06-01
发表期刊	SET-VALUED AND VARIATIONAL ANALYSIS
ISSN	1877-0533
卷号	25 期号:2 页码:265-296
摘要	In this paper, we will study some variational properties of the Ky Fan k-norm theta = parallel to . parallel to((k)) of matrices, which are closed related to a class of basic nonlinear optimization problems involving the Ky Fan k-norm. In particular, for the basic nonlinear optimization problems, we will introduce the concept of nondegeneracy, strict complementarity and the critical cones associated with the generalized equations. Finally, we present the explicit formulas of the conjugate function of the parabolic second order directional derivative of oee integral, which will be referred to as the sigma term of the second order optimality conditions. The results obtained in this paper provide the necessary theoretical foundations for future work on sensitivity and stability analysis of the nonlinear optimization problems involving the Ky Fan k-norm.
关键词	Ky Fan k-norm Nondegeneracy Critical cone Second order tangent sets
DOI	10.1007/s11228-016-0378-3
语种	英语
资助项目	National Natural Science Foundation of China[11301515]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000401354700004
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25432
专题	应用数学研究所
通讯作者	Ding, Chao
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Ding, Chao. Variational Analysis of the Ky Fan k-norm[J]. SET-VALUED AND VARIATIONAL ANALYSIS,2017,25(2):265-296.
APA	Ding, Chao.(2017).Variational Analysis of the Ky Fan k-norm.SET-VALUED AND VARIATIONAL ANALYSIS,25(2),265-296.
MLA	Ding, Chao."Variational Analysis of the Ky Fan k-norm".SET-VALUED AND VARIATIONAL ANALYSIS 25.2(2017):265-296.