集值优化问题的E-Henig真有效解

E-Henig Proper Efficient Solution for Set-Valued Optimization Problems

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.