| 非光滑广义Dini-凸多目标规划解的充分性与对偶性 |
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| 引用本文： | 康瑞瑞,张庆祥,姜艳,张文静. 非光滑广义Dini-凸多目标规划解的充分性与对偶性[J]. 郑州大学学报(自然科学版), 2012, 0(2): 13-19 |
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| 作者姓名： | 康瑞瑞 张庆祥 姜艳 张文静 |
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| 作者单位： | [1]北京交通大学理学院,北京100044 [2]延安大学数学与计算科学学院,陕西延安716000 |
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| 基金项目： | 国家自然科学基金资助项目,编号61071144;陕西省教育厅专项科研基金资助项目,编号06JKl52. |
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| 摘 要： | 利用Ben-Tal广义代数运算,给出了一种新的广义Dini右上方向导数和广义Dini梯度,引进了几类非光滑非凸函数的概念,在较弱的假设下,给出了广义Dini不变凸函数的一个充要条件,得到了非光滑广义Dini-凸多目标规划的最优性充分条件和几个对偶性结果.
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| 关 键 词： | 非光滑 Dini-凸函数 多目标规划 充分性 对偶性 |
On Sufficiency and Duality of Solutions for Nonsmooth Generalized Dini-convex Multiobject Programming |
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| KANG Rui-rui ZHANG,Qing-xiang,JIANG Yan,ZHANG Wen-jing. On Sufficiency and Duality of Solutions for Nonsmooth Generalized Dini-convex Multiobject Programming[J]. Journal of Zhengzhou University (Natural Science), 2012, 0(2): 13-19 |
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| Authors: | KANG Rui-rui ZHANG Qing-xiang JIANG Yan ZHANG Wen-jing |
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| Affiliation: | 1. College of Science, Beijing Jiaotong University, Beijing 100044, China ; 2. College of Mathematics and Computer Science, Yah＇ an University, Yah＇ an 716000, China) |
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| Abstract: | The generalized upper right directional Dini-derivative and Dini-gradient were given by using Ben-Tal＇ s generalized algebraic operations. Several classes of nonsmooth nonconvex functions （ general- ized Dini-convex） were introduced. Based on weaker assumptions, a sufficient and necessary condition for generalized Dini-invex functions was given, some optimal sufficient conditions and duality were ob- tained for a class of nonsmooth generalized Dini-convex multiobject programming. |
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| Keywords: | nonsmooth Dini-convex function multiobject programming sufficiency duality |
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