集值优化中扰动映射的二阶S导数的灵敏度分析

Sensitivity for the second-order S-derivative of the perturbation map in set-valued optimization

引进一种新的二阶切导数,称为二阶S导数,并讨论它的性质以及它与二阶切导数的关系。借助二阶S导数,建立集值映射切导数的极小值与扰动映射切导数之间的关系。

In this paper,a new kind of second-order contingent derivative is introduced,termed second-order S-derivative.Some properties of second-order S-derivative and the relationship to second-order contingent derivative are discussed.Then,with the help of second-order S-derivative,relationships are established between the minimum of contingent derivative of set-valued maps and contingent derivative of perturbation maps.