| 集值映射的Epi-导数及其应用 |
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| 引用本文： | 王明征,夏尊铨.集值映射的Epi-导数及其应用[J].运筹学学报,2003,7(3):45-55. |
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| 作者姓名： | 王明征 夏尊铨 |
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| 作者单位： | 大连理工大学应用数学系,大连,116024 |
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| 基金项目： | Partly supported by the State Foundations of Ph.D Units(20020141013), NSF of China(10001007)，the DUT Foundations of Young Teachers No3004-893203. |
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| 摘 要： | 在本文里，集值映射的Epi-导数被引入，它可以认作是实值Lipschitz函数的Clarke-广义方向导数的推广，同时它的一些性质也被研究．进一步地，利用这个Epi-导数集值映射的次微分被定义并研究它的性质．作为其应用，我们给出了集值优化问题的一些(必要或充分)最优性条件．
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| 关 键 词： | 集值映射 Epi-导数 应用 Lipschitz函数 Clarke-广义方向导数 次微分 集值优化 |
On an Epiderivative of Set-Valued Maps and Its Application |
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| MINGZHENG WANG ZUNQUAN XIA.On an Epiderivative of Set-Valued Maps and Its Application[J].OR Transactions,2003,7(3):45-55. |
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| Authors: | MINGZHENG WANG ZUNQUAN XIA |
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| Abstract: | An epiderivative for a set-valued map is introduced in this paper that can be regarded as an extension to Clarke generalized directional derivative for a real-valued Lipschitz function and its properties are discussed. Furthermore, the subdifferential of a general set-valued map is defined in terms of this epiderivative. As an application, some (necessary and/or sufficient) optimality conditions of set-valued optimization problems are presented based on obtained results. |
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| Keywords: | OR epiderivative set-valued map set-valued optimization set-valued analysis subdifferential optimality conditions |
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