| 集值优化问题$\varepsilon-$强有效解的最优性条件 |
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| 引用本文： | 余丽.集值优化问题$\varepsilon-$强有效解的最优性条件[J].福州大学学报(自然科学版),2015,43(1). |
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| 作者姓名： | 余丽 |
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| 摘 要： | 在Hausdorff局部凸拓扑向量空间中引入集值映射$\varepsilon-$强有效次梯度和$\varepsilon-$强有效次微分的概念.在一定条件下,利用凸集分离定理证明了该次微分(次梯度)的存在性及它的一些性质.作为应用,对于一类参数扰动集值优化问题讨论了其在 $\varepsilon-$强有效意义下的稳定性.
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| 关 键 词： | 集值优化 $\varepsilon-$强有效性 次微分 次梯度 稳定性 |
| 收稿时间： | 3/7/2013 12:00:00 AM |
| 修稿时间： | 4/2/2013 12:00:00 AM |
Optimality Conditions of $\varepsilon-$Strongly Efficient Solutions for Set-valued Optimization Problem |
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| YULI.Optimality Conditions of $\varepsilon-$Strongly Efficient Solutions for Set-valued Optimization Problem[J].Journal of Fuzhou University(Natural Science Edition),2015,43(1). |
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| Authors: | YULI |
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| Institution: | Institute of Mathematics and Computer of Science ,Yichun University, Jiangxi, Yichun 336000 |
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| Abstract: | In Hausdorff locally convex topological vector spaces, the concepts of $\varepsilon-$strongly efficient subgradient and $\varepsilon-$ strongly efficient subdifferential for a set-valued mapping are introduced.
Under certain conditions, by using the convex set separation theorem, the existence theorem for $\varepsilon-$ strongly efficient subgradient($\varepsilon-$ strongly efficient subdifferential) is proposed. As an application, the stability problem for a kind of perturbed set-valued optimization problem is considered in the sense of $\varepsilon-$strongly efficiency. |
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| Keywords: | set-valued optimization ~$\varepsilon-$strongly efficiency ~subdifferential ~subgradient ~stability |
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