一类向量极值问题的最优性条件和Lagrange对偶  

Optimality Conditions and Lagrange Duality for a Class of Vector Extremum Problems

作　　者：王其林[1] 李泽民[2] 

机构地区：[1]重庆交通学院基础部,重庆400074 [2]重庆大学数理学院,重庆400030

出　　处：《重庆大学学报（自然科学版）》2005年第6期106-109,共4页Journal of Chongqing University

基　　金：重庆交通学院科研基金资助课题(人才2004-02-20)

摘　　要：在序局部凸Hausdorff空间中利用广义次似凸映射下的择一定理,得出带集合约束的向量极值问题的一个最优性充要条件.利用此充要条件和二次G-可微函数的性质,获得了可微向量极值问题的几个最优性条件.最后,得到了此类向量极值问题的向量值Lagrange对偶.A sufficient and necessary optimality conditions is established for vector extremum problems with set constraint by applying the alternative theorem under generalized subconvexlike maps in orderd locally-convex Hausdorff spaces. Then, several optimality conditions are obtained for differentiable vector extremum problems with set constraint by applying the sufficient and necessary optimality conditions and the properties of the twice G-differentiable functions. And finally, the vector-valued Lagrange duality is obtained for the vector extremum problems.

关 键 词：广义次似凸 择一定理 最优性条件 向量值Lagrange对偶 

分 类 号：O221[理学—运筹学与控制论]