| 一类广义univex条件下的多目标规划 |
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| 引用本文： | 程曹宗,张瑞芳.一类广义univex条件下的多目标规划[J].北京工业大学学报,2012,38(3):467-472. |
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| 作者姓名： | 程曹宗 张瑞芳 |
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| 作者单位： | 北京工业大学应用数理学院,北京,100124 |
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| 基金项目： | 国家自然科学基金资助项目，北京工业大学自然科学基础研究资助项目 |
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| 摘 要： | 引入了一种新的广义不变凸函数,即d-ρηθ-univex函数,讨论了这一概念与d-不变凸函数、d-univex函数、d-ρηθ-不变凸函数之间的关系,并在d-ρηθ-univex条件下考察一类多目标规划问题(P).首先给出问题(P)的弱Pareto有效解存在的充分条件;进而得到问题(P)的Mond-Weir型对偶的弱对偶、强对偶和逆对偶结论以及问题(P)的广义Mond-Weir型对偶的弱对偶和强对偶论断.
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| 关 键 词： | d-ρηθ-univex函数 多目标规划 Pareto有效解 Mond-Weir对偶 广义Mond-Weir对偶 |
Multiobjective Programming Under a Class of Generalized Univexity |
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| CHENG Cao-zong,ZHANG Rui-fang.Multiobjective Programming Under a Class of Generalized Univexity[J].Journal of Beijing Polytechnic University,2012,38(3):467-472. |
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| Authors: | CHENG Cao-zong ZHANG Rui-fang |
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| Affiliation: | (College of Applied Sciences,Beijing University of Technology,Beijing 100124,China) |
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| Abstract: | This paper introduces a new class of generalized invex function called d-ρηθ-univex function,and discusses the relationship among d-invex,d-univex,d-ρηθ-invex,and d-ρηθ-univex functions.Under d-ρηθ-univexity assumption,one type of multiobjective programming problem(P) is considered.The sufficient optimality conditions for the existence of the weak Pareto efficient solution of the problem(P) are first established.The results on the weak,strong and converse duality of Mond-Weir type duality,and the weak and strong duality assertions of the generalized Mond-Weir type duality of the problem(P) are then obtained. |
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| Keywords: | d-pηθ-univex function multiobjective programming Pareto efficient solution Mond-Weirduality generalized Mond-Weir duality |
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