R^n上的γ-次微分与γ-凸性

γ subdifferential and γ convexity of Functions on the R n

提出了Ｒｎ上的γ－次微分与γ－凸性的概念．利用γ－次微分给出了许多局部极小（极大）不能满足的全局极小（极大）的一个新的必要条件．利用γ－凸性给出了全局极小的充分条件，且γ－凸函数的局部极小总是全局极小．

In this paper the γ subdifferential and γ convexity of realvalued functions on the R n were introduced. By means of the γ subdifferential a new necessary condition for global minima is formulated which many local minima cannot satisfy.The γ convexity is used to state sufficient conditions for global minima. The γ convex function is relatively large.For example,there are γ convex functions which are not continuous anywhere. Nevertheless,a local minimum of a γ convex function is always a global minimum.