Star-kernels and star-differentials in quasidifferential analysis
Zhang, LW; Xia, ZQ; Gao, Y; Wang, MZ
AbstractThis 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.
Keywordquasidifferentiable function directional derivative quasidifferential kernelled quasidifferential star-kernel star-differential star-shaped set
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000177413600007
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Document Type期刊论文
Corresponding AuthorZhang, LW
Affiliation1.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
Recommended Citation
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.
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