集值优化问题的Henig真有效解的最优性条件  

The Optimization Condition of Henig Proper Efficient Solution for Set-valued Optimization Problem

作　　者：李文敏[1] 高国荣[1] 韩有攀[2] 

机构地区：[1]西北农林科技大学理学院,陕西杨凌712100 [2]西安交通大学理学院,西安710049

出　　处：《河南师范大学学报（自然科学版）》2010年第1期1-4,共4页Journal of Henan Normal University(Natural Science Edition)

基　　金：西北农林科技大学人才引进基金(01140407)

摘　　要：在线性拓扑空间中,首先给出集值映射为近似锥次类凸时的择一性定理,利用此定理,得到了集值优化问题的Henig真有效解的Lagrange型最优性条件,进而,给出了它的一个充要条件.然后,利用锥凸分离定理得到了Henig真有效解的Kuhn-Tucker型最优性条件,同时给出了相应的充分条件和充要条件.In linear topological space ,the alternative theorem is proposed under the condition that set-valued map is nearly cone-subconvexlikeness.By the aid of the alternative theorem,the Lagrange type optimality condition for the set-valued optimization problem with constraints is obtained.The sufficient and necessary conditions of the problem is also established.Then by applying separation theorem for convex sets,the Kuhn-Tucker optimality condition is given,and meanwhile the corresponding sufficient condition and the corresponding sufficient and necessary conditions are also obtained.

关 键 词：集值映射 近似锥次类凸 Henig真有效解 最优性 

分 类 号：O224[理学—运筹学与控制论]