集合最优化问题的Lagrange对偶  

Lagrangian Duality for Set Optimization Problem

作　　者：李毛亲[1] 李杉林[1] 

机构地区：[1]台州学院数学系,浙江临海317000

出　　处：《中北大学学报（自然科学版）》2011年第4期392-397,共6页Journal of North University of China(Natural Science Edition)

基　　金：山西省留学回国人员基金资助项目(2010087);浙江省台州学院培育基金资助项目(2010PY112011PY06)

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.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.

关 键 词：集合最优化 下关系 Cy-次类凸 Lagrangian对偶 鞍点 

分 类 号：O221.6[理学—运筹学与控制论] C931.1[理学—数学]