集值优化局部严极小元的二阶必要条件  

Second-order necessary optimality conditions for local strict minimizer of set-valued optimization Problem

作　　者：张爱红[1] 徐义红[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2014年第3期303-306,共4页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(11461044);江西省自然科学基金资助项目(20122BAB201003);江西省教育厅科技资助项目(GJJ12010)

摘　　要：在实赋范线性空间中考虑带包含约束的集值优化问题(P)。给出了集值优化问题局部严极小元概念,在方向度量正则假设下,利用扩张锥及扩张锥内部的性质借助二阶下导数给出了(P)取得局部严极小元的必要条件。Set-valued optimization with inclusion constraint in real normed linear spaces was considered. The concept of locally strict minimizer for set-valued optimization was introduced. Under the hypothesis of directional metric regular dilating , a second-order necessary optimality cone and the properties of interior dilating condition for locally strict minimizer was established by using the cone with the help of second-order lower derivative.

关 键 词：局部严极小元 二阶导数 集值优化 

分 类 号：O224[理学—运筹学与控制论]