半预不变凸集值向量优化问题的弱极小解  

Weak Minimal Solutions in the Vector Optimization of Set-Valued Maps with Semi-Preinvexity

作　　者：郭高[1] 赵东涛[2] 

机构地区：[1]西安理工大学理学院,陕西西安710048 [2]第四军医大学生物医学工程系,陕西西安710032

出　　处：《西安理工大学学报》2010年第4期464-467,共4页Journal of Xi'an University of Technology

基　　金：陕西省教育厅科技专项基金资助项目(09JK615)

摘　　要：将单值映射的半预不变凸概念推广到集值映射,建立了半预不变凸集值映射的择一定理,并应用择一定理获得了半预不变凸集值映射向量优化问题的最优性必要条件,建立了两个Lagrange乘子定理和Lagrange对偶定理。This research extends the concept of cone semi-preinvex of single-valued maps to set-valued maps and presents an alternative theorem for cone semi-preinvex of set-valued maps.And then the necessary optimality condition for the vector optimization problem of semi-preinvex set-valued maps is obtained by applying the alternative theorem.Two lagrange multiplier theorems and lagrange duality theorems are established finally.

关 键 词：最优化 最优性必要条件 择一定理 半预不变凸集值映射 对偶 

分 类 号：O224[理学—运筹学与控制论]