预不变凸规划问题解集的刻画

Characterizations of the Solution Sets of Preinvex Programming

本文在不变凸集上定义了预不变凸函数的方向导数、η-近似次微分和η-Gateaux可微的概念,证明了预不变凸函数的η-近似次微分的一些性质,并在此基础上得到了预不变凸规划问题解集的等价刻画。

Directional derivative, η-proximal subdifferential and η-Gateaux differentiable of preinvex functions are defined on the invex set. Some properties of η-proximal subdifferential of preinvex functions are obtained. Under these conditions, we obtained the equivalent characterizations of the solution sets of preinvex programming.