| 集值优化问题的二阶最优性条件 |
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| 引用本文： | 王学永,朱胜坤,彭兴媛.集值优化问题的二阶最优性条件[J].四川大学学报(自然科学版),2012,49(6):1181-1188. |
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| 作者姓名： | 王学永 朱胜坤 彭兴媛 |
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| 作者单位： | 重庆大学数学与统计学院,重庆,401331 |
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| 基金项目： | 中央高校基本科研业务费资助项目(CDJXS11100034) |
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| 摘 要： | 本文提出了集值映射的一种二阶导数,并讨论了其相关性质.运用此二阶导数以及二阶相依导数,作者建立了实赋范空间中集值优化问题的二阶必要最优性条件;同时,在有限维赋范空间中,建立了集值优化问题的二阶充分最优性条件.
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| 关 键 词： | 二阶相依集 二阶渐近相依导数 集值优化 最优性条件 |
| 收稿时间： | 2011/10/11 0:00:00 |
Second-order optimality conditions in set-valued optimization problems |
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| WANG Xue-Yong,ZHU Sheng-Kun and PENG Xing-Yuan.Second-order optimality conditions in set-valued optimization problems[J].Journal of Sichuan University (Natural Science Edition),2012,49(6):1181-1188. |
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| Authors: | WANG Xue-Yong ZHU Sheng-Kun and PENG Xing-Yuan |
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| Institution: | College of Mathematics and Statistics, Chongqing University;College of Mathematics and Statistics, Chongqing University;College of Mathematics and Statistics, Chongqing University |
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| Abstract: | In this paper, a second order derivative for set valued maps is proposed and its properties are discussed. By using this derivative and second order contingent derivative, some second order necessary optimality conditions for set valued optimization problems in real normed spaces are obtained. Simultaneously, some second order sufficient optimality conditions for set valued optimization problems in finite dimensional normed spaces are established. |
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| Keywords: | second-order contingent set second-order asymptotic contingent derivative set-valued optimization optimality condition |
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