二阶渐近切上图导数及应用

Second-Order Asymptotic Epiderivative and Application

在实赋范线性空间中利用新定义的二阶渐近切上图导数研究集值优化问题的严有效性.通过二阶渐近切锥引进一种新的二阶渐近切上图导数,给出一个例子说明它的存在条件比二阶渐近切导数存在条件更弱,并利用此导数及扩张锥的性质给出了集值优化问题取得局部严有效元的必要条件.

The strict efficiency of set-valued optimization was considered in real normed linear space by a new second-order asymptotic epiderivative.With the help of second-order asymptotic tangent cone, a new second-order asymptotic epiderivative was introduced.At the same time,an example was given to show that its existence condition is weaker than that of second-order asymptotic tangent derivative. By applying the derivative and properties of a dilating cone,an optimality necessary condition of locally strictly efficient element for set-valued optimization was established.