| 集值优化问题严格有效解的一、二阶最优性条件 |
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| 引用本文： | 柴艳飞,刘三阳,李军.集值优化问题严格有效解的一、二阶最优性条件[J].数学物理学报(A辑),2014,34(1):193-206. |
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| 作者姓名： | 柴艳飞 刘三阳 李军 |
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| 作者单位： | 西安电子科技大学数学与统计学院系 西安 710071；西华师范大学数学与信息学院 四川 南充 637002 |
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| 基金项目： | 国家自然科学基金(61373174, 11371015)、教育部科学技术重点项目(211163)和四川省青年科技基金(2012JQ0032)资助. |
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| 摘 要： | 首先定义了集值优化问题的m阶局部严格有效解并在赋范空间中研究了解的一些性质.在一定条件下,利用Dini导算子和支撑函数确立了m≥1阶严格有效解存在的充分必要条件.
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| 关 键 词： | 集值优化 一、二阶最有性条件 支撑函数 严格最优解 Dini导算子 切锥 |
| 收稿时间： | 2012-04-07 |
| 修稿时间： | 2013-08-17 |
First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization |
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| LIU San-Yang,LI Jun.First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization[J].Acta Mathematica Scientia,2014,34(1):193-206. |
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| Authors: | LIU San-Yang LI Jun |
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| Institution: | Department of Applied Mathematics, Xidian University, Xi'an |710071； School of Mathematics and Information, China West Normal University, Sichuan Nanchong |637002 |
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| Abstract: | In this paper, the notion of local strict minimum of order m (m≥1) for vector optimization problems is extended
from single-valued maps to set-valued maps. Some properties and characterizations are then investigated in normed spaces. Furthermore, necessary and sufficient conditions for strict minimum of orders m≥1 are established by using Dini derivatives and support functions. |
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| Keywords: | Set-valued optimizationzz First and second order optimalityzz Support functionzz Strict minimumzz Dini derivativezz Tangent conezz |
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