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

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.