Star-kernels and star-differentials in quasidifferential analysis
文献类型：期刊论文
| 作者 | Zhang, LW; Xia, ZQ; Gao, Y; Wang, MZ |
| 刊名 | JOURNAL OF CONVEX ANALYSIS
 |
| 出版日期 | 2002 |
| 卷号 | 9期号:1页码:139-158 |
| 关键词 | quasidifferentiable function directional derivative quasidifferential kernelled quasidifferential star-kernel star-differential star-shaped set |
| ISSN号 | 0944-6532 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000177413600007 |
| 出版者 | HELDERMANN VERLAG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/17648]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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