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数学与物理
应用数学进展
Vol. 5 No. 3 (August 2016)
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集值优化问题的E-Henig真有效解
E-Henig Proper Efficient Solution for Set-Valued Optimization Problems
DOI:
10.12677/AAM.2016.53060
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被引量
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国家自然科学基金支持
作者:
林佩静
,
仇秋生
:浙江师范大学,浙江 金华;
李茂旺
:江西冶金职业技术学院,江西 新余
关键词:
E-Henig真有效解
;
标量化
;
真鞍点
;
对偶
;
E-Henig Proper Efficient Solution
;
Scalarization
;
Proper Saddle Point
;
Duality
摘要:
本文研究集值优化问题的E-Henig真有效解。首先,在实局部凸Hausdoff空间中引进了E-Henig真有效点的概念,给出了E-Henig真有效点的等价刻画,讨论了它与E-Benson真有效点和E-超有效点的关系。其次,在集值映射为近似E-次类凸的条件下,建立了E-Henig真有效解的标量化定理。最后,研究了E-Henig真有效解的鞍点定理和对偶定理。
Abstract:
In this paper, we study E-Henig proper efficient solution for set-valued optimization problem. Firstly, the concept of E-Henig proper efficient point in a real Hausdorff locally convex space is given. The relationships with E-Benson proper point and E-super point are discussed. Secondly, under the assumption of nearly subconvexlikeness, scalarization theorems of E-Henig proper efficient solution are established. Lastly, E-Henig saddle point theorem and E-Henig duality theorem are studied.
文章引用:
林佩静, 李茂旺, 仇秋生. 集值优化问题的E-Henig真有效解[J]. 应用数学进展, 2016, 5(3): 494-504.
http://dx.doi.org/10.12677/AAM.2016.53060
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