集值优化问题的E-Henig真有效解
E-Henig Proper Efficient Solution for Set-Valued Optimization Problems
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 (2016) 集值优化问题的E-Henig真有效解。 应用数学进展， 5， 494-504. doi: 10.12677/AAM.2016.53060
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