ε一次微分的若干性质及二阶(G)可微的一个等价形式

Some Properties of ε-Subdifferential and an Equivalent Form of Second Gateaux Differentiable

本文在线性拓扑空间中建立了泛函的(LP)条件(Lipschitz条件),在此基础上讨论了广义方向导数及它的次微分。给出了凸泛函的二阶(G)可微的一个等价形式。同时,还研究了ε一次微分的有关问题。

Lipschitz's condition of functional is put forward in a linear topological space. On this basis,generalized directional derivative and its subdifferential are discussed. An equivalent form on second Gateaux differentiable is obtained. Meanwhile,ε-subdifferential is studied.