集值优化问题的广义梯度与ε-全局真有效解的最优性条件  

Generalized Gradient of Set-valued Optimization Problems and Optimality Conditions of ε-Globally Proper Efficient Solutions

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：《四川师范大学学报（自然科学版）》2013年第1期44-47,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：江西省自然科学基金(20122BAB211004)资助项目

摘　　要：由于集值优化理论的近似有效解与Ekeland变分原理之间存在紧密的联系,因此,在实赋范线性空间中利用集值映射的上图导数引进了ε-全局真有效意义下的广义梯度的概念,在连通性条件下通过凸集分离定理证明了该广义梯度的存在性,并给出了用广义梯度刻画集值优化问题ε-全局真有效解的充分和必要条件.Based on the close relation between the approximate efficient solutions and the well-known Ekeland variational principle, a concept of generalized gradient in sense of ε- globally proper efficiency is introduced by epiderivative for a set-valued mapping in a real normed linear space. Under the connectivity condition, its existence is derived by the separation theorem for convex sets. As an application, the optimality necessary and sufficient conditions of ε-globally proper efficient solution for set-valued optimization problem are established in terms of the generalized gradient.

关 键 词：切导数 ε-全局真有效性 广义梯度 最优性条件 

分 类 号：O224[理学—运筹学与控制论]