凸函数与超加函数的关系研究

A note on convex functions and superadditive functions

应用积分理论,研究了在整数规划中具有重要应用的凸函数及其超加函数的关系.利用超加函数的有关结论,证明了任何过原点的凸函数必为超加函数,并得到了此类凸函数的若干推论.

By using integral theory, this paper presents the discussion of the relationship between convex functions and superadditive functions which are very useful in the theory of integer programming. On the basis of the result on superadditive functions, it is proved that every passingzero convex function must be superadditive, and some deductions are obtained on this convex function.