中文摘要：

在偏序拓扑线性空间,讨论了具有集值映射的最优化问题的L agrange对偶和鞍点问题.该最优化问题解的判别依赖于目标空间集合之间的下关系.对于给定的具有线性乘子的L agrange集值映射,在公理化对偶的框架下,得到了弱对偶定理;在CY-次类凸的条件下得到了强对偶定理.给出了鞍点存在的必要条件和充分条件,同时通过鞍点得到了集合最优化问题解的存在性条件.

英文摘要：

In partially ordered topological linear space,Lagrangian duality and saddle points of the set optimization problem were concerned,where the solutions to the problem are identified by set criterion.For a given Lagrangian map with linear multiplier,a weak duality theorem was obtained under the frame of axiomatic duality principles;and a strong duality theorem was developed under the condition of CY-subconvexlikeness.A sufficient condition and a necessary condition of the existence of saddle points were given.Through these saddle points,the existence conditions of solution to the set optimization problem were presented.