| 集值映射的广义梯度与超有效解 |
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| 引用本文： | 侯震梅,周勇. 集值映射的广义梯度与超有效解[J]. 吉林大学学报(理学版), 2006, 44(1): 9-14 |
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| 作者姓名： | 侯震梅 周勇 |
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| 作者单位： | 新疆财经学院,统计与信息系,乌鲁木齐,830012;西安电子科技大学,应用数学系,西安,710071;新疆财经学院,统计与信息系,乌鲁木齐,830012;西安电子科技大学,应用数学系,西安,710071 |
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| 摘 要： | 在锥序Banach空间中引入了一类集值映射的广义梯度，在一定条件下通过凸集分离定理证明了此广义梯度的存在性； 并给出集值优化问题的超有效解在广义梯度下的最优条件.
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| 关 键 词： | 集值优化 切导数 超有效性 广义梯度 |
| 文章编号： | 1671-5489(2006)01-0009-06 |
| 收稿时间： | 2005-01-24 |
| 修稿时间： | 2005-01-24 |
Generalized Gradient of Set-valued Mapping and Super-efficient Solution |
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| HOU Zhen-mei,ZHOU Yong. Generalized Gradient of Set-valued Mapping and Super-efficient Solution[J]. Journal of Jilin University: Sci Ed, 2006, 44(1): 9-14 |
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| Authors: | HOU Zhen-mei ZHOU Yong |
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| Affiliation: | 1. Department of Statistics and Information, Xinjiang Institute of Finance and Economics, Urumqi 830012, China;2. Department of Applied Mathematics, Xidian University, Xi’an 710071, China |
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| Abstract: | The generalized gradient of a kind of set-valued mappings is introduced into ordered Banach spaces and under certain conditions its existence is proved via the separation theorem.The optimality conditions of (super)-efficient solution of set-valued optimization problems are presented in the sense of generalized gradient. |
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| Keywords: | set-valued optimization contingent derivative super-efficiency generalized gradient |
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