中文摘要：

利用Ben-Tal广义代数运算,给出了一种新的广义Dini右上方向导数和广义Dini梯度,引进了几类非光滑非凸函数的概念,在较弱的假设下,给出了广义Dini不变凸函数的一个充要条件,得到了非光滑广义Dini-凸多目标规划的最优性充分条件和几个对偶性结果.

英文摘要：

The generalized upper right directional Dini-derivative and Dini-gradient were given by using Ben-Tal＇ s generalized algebraic operations. Several classes of nonsmooth nonconvex functions （ general- ized Dini-convex） were introduced. Based on weaker assumptions, a sufficient and necessary condition for generalized Dini-invex functions was given, some optimal sufficient conditions and duality were ob- tained for a class of nonsmooth generalized Dini-convex multiobject programming.