一类新的Fenchel共轭函数

A NEW CLASS OF FENCHEL DUALITY

本文把Fenchel对偶由下半连续凸函数推广到局部Lipschitz函数,得到任一个下半连续函数可表示为一个局部Lipschitz函数与一个凸函数差的上包络;同时,下半连续函数的光滑性也可借助强极小值点进行等价刻划.

In this paper, we extend the Fenchel duality from the proper lower semi-continuous function to the local Lipschitz function and obtain a lower semi-continuous function may be denoted by a local Lipschitz function and a convex function. Furthermore, we achieve the strongly minimal point can describe the smooth property of the lower semi-continuous function.