集值映射的ε-强次微分及应用  

ε-strongly subdifferential of set-valued mapping and application

作　　者：余丽[1] 

机构地区：[1]宜春学院数学与计算机科学学院,江西宜春336000

出　　处：《山东大学学报（理学版）》2013年第3期99-105,共7页Journal of Shandong University(Natural Science)

基　　金：江西省自然科学基金资助项目(0611081)

摘　　要：在Hausdorff局部凸拓扑向量空间中引进了集值映射ε-强有效次微分的概念。在一定条件下,通过凸集分离定理证明了该次微分的存在性定理。作为应用,得到了约束集值优化问题ε-强有效解在Lagrange乘子形式下的最优性必要条件。In Hausdorff locally convex topological vector spaces, the concept of ε-strongly efficient subdifferential for a set-valued mapping was introduced. Under certain condition, by using the convex set separation theorem, the existence theorem for ε-strongly efficient subdifferential was proposed. As an application, the necessary optimality condition of the constraint set-valued optimization problem for ε-strongly efficient solutions was established in terms of Lagrange multiplier by using the concept of ε-strongly efficient subdifferential for set-valued mapping.

关 键 词：ε-强有效性 次微分 LAGRANGE乘子 最优性条件 

分 类 号：O221[理学—运筹学与控制论] O224[理学—数学]