摘要
本文讨论了可微的强invex函数和强pseudoinvex函数分别与其梯度的强不变单调和强不变伪单调的关系,得到了pseudoinvex函数在某些条件下可以等价prequasiinvex函数.证明了:若f关于向量值函数η是preinvex函数,且满足lipschitz条件,则y为f(x)的全局极小点等价于0∈?0f(y).
The relation between differential strongly invex （pseudoinvex） functions and the stongly invariant monotone （pseudomonotone） of their gradients is discussed. It is obtained that a function f（x） is pseudoinvex with respect to a vector function η iff it is prequasiinvex with respect to the same vector function η when it satisfies some conditions, and it is showed that a point y is the global minimal point of f（x） iff 0∈（e）^0f（y） if f is a preinvex function with respect to a vector function η.
出处
《漳州师范学院学报（自然科学版）》
2005年第3期1-7,共7页
Journal of ZhangZhou Teachers College（Natural Science)
关键词
强不变单调
强不变伪单调
广义次梯度
广义方向导数
Stongly invariant monotone
stongly invariant pseudomonotone
general gradient
generally directional derivative
