Star-kernels and star-differentials in quasidifferential analysis

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	Star-kernels and star-differentials in quasidifferential analysis
	Zhang, LW ; Xia, ZQ ; Gao, Y ; Wang, MZ
	2002
发表期刊	JOURNAL OF CONVEX ANALYSIS
ISSN	0944-6532
卷号	9 期号:1 页码:139-158
摘要	This paper is devoted to the study of quasidifferential structure. Three concepts, kernelled quasidifferential, star-kernel and star-differential, are proposed. Kernelled quasidifferential is used to describe a special class of quasidifferentiable functions, which covers convex and concave functions. A sufficiency theorem and a sufficiency and necessity theorem for a quasi-kernel being a kernelled quasidifferential are proven. The notion of star-kernel is employed if the quasi-kernel is not a kernelled quasidifferential. The existence theorem for a star-kernel of a quasidifferentiable function is established, which shows that the star-kernel is a pair of star-shaped sets and the sub-/super-derivative is expressed by the gauge of a star-shaped set. The notion of star-differential is used to describe the differential of the class of directionally differentiable functions which contains the class of quasidifferentiable functions. A star-differential is also a pair of star-shaped sets and its operational properties are favourable. A representative of the star-differential can be easily obtained by decomposing the directional derivative into the difference of its positive and negative part.
关键词	quasidifferentiable function directional derivative quasidifferential kernelled quasidifferential star-kernel star-differential star-shaped set
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000177413600007
出版者	HELDERMANN VERLAG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17649
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, LW
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Dalian Univ Technol, Dept Appl Math, CORA, Dalian 116024, Peoples R China 3.Shanghai Univ Sci & Technol, Sch Management, Shanghai 200093, Peoples R China
推荐引用方式 GB/T 7714	Zhang, LW,Xia, ZQ,Gao, Y,et al. Star-kernels and star-differentials in quasidifferential analysis[J]. JOURNAL OF CONVEX ANALYSIS,2002,9(1):139-158.
APA	Zhang, LW,Xia, ZQ,Gao, Y,&Wang, MZ.(2002).Star-kernels and star-differentials in quasidifferential analysis.JOURNAL OF CONVEX ANALYSIS,9(1),139-158.
MLA	Zhang, LW,et al."Star-kernels and star-differentials in quasidifferential analysis".JOURNAL OF CONVEX ANALYSIS 9.1(2002):139-158.