回收函数与函数的性态研究

Some Results on Recession Functions and Properties of Functions

本文通过研究正常凸函数的回收函数,讨论了正常凸函数的回收方向与极小值之间的关系,并得到了函数的性态及极值存在性的刻画.借助回收方向得出了该函数在无约束集合和约束集合上是否取得的极小值的一些相关结果.

By studying the recession functions of proper convex functions, the relationship between the recession direction of proper convex function and its minimal value is discussed. The properties of the function and the existence of its minimal value are characterized. At the same time, some corresponding conclusions about the existence of this minimal value on constraint set and unconstraint set are obtained with the help of recession direction.