关于次微分convexificator与exhauster关系的一个结果

A Result on the Relation of Subdifferential Convexificator and Exhauster

从次微分convexificator和exhauster的概念出发,在局部Lipschitz条件下,应用函数的上凸(下凹)逼近的exhaustive族存在性定理,并结合已有的相关结论,得出必存在上exhauster和上半正则convexificator,分别记为E*h和坠*f(x),使得坠*f(x)∈E*h.

From the subdifferential concepts of convexificator and exhauster under the condition of Lipschitz and by applying the existence theorem of exhaustive families of upper convex and lower concave approximations as well as the relative results, a conclusion is drawn that there should exist upper exhauster and upper-half regular convexificator, i.e., E＊h and ＊f（x） with the relation of ＊ f（x）∈E＊h.