集-集映射向量极值问题的Lagrange乘子和鞍点定理

Lagrange Multiplier and Saddle Point Theorems of Vector Extreme Value Problem with Set-Set Maps

本文先建立了集－集映射的一个广义择一性定理．在目标为锥凸和满足 推广了的Ｓｌａｔｅｒ约束规格的条件下，我们利用本文的择一性定理，给出了集一集映射 向量极值问题关于锥－超极小解的Ｌａｇｒａｎｇｅ乘子定理和鞍点定理．

In this paper, a generalized alternative theorem for set-set maps is established. Under cone convexity assumptions and assume the generalized Slater constraint qualification is satisfied, by applying this alternative theorem, we give Lagrange multiplier theorem and saddle point theorem of cone-super minimum solution for vector extreme value problem with set-set maps.