本文共 904 字，大约阅读时间需要 3 分钟。

詹森不等式以丹麦数学家约翰·詹森（Johan Jensen）命名。它给出积分的凸函数值和凸函数的积分值间的关系。

In , Jensen's inequality, named after the Danish mathematician , relates the value of a  of an  to the integral of the convex function. It was proven by Jensen in 1906. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations.

Jensen不等式是关于凸性(convexity)的不等式。凸性是非常好的性质，在最优化问题里面，线性和非线性不是本质的区别，只有凸性才是。如果最优化的函数是凸的，那么局部最优就意味着全局最优，否则无法推得全局最优。有很多不等式都可以用Jensen不等式证得，从而可以把他们的本质归结为凸性。例如，均值不等式。

1. C++标准模板库从入门到精通 

2.跟老菜鸟学C++

3. 跟老菜鸟学python

4. 在VC2015里学会使用tinyxml库

5. 在Windows下SVN的版本管理与实战 

转载地址：https://mysoft.blog.csdn.net/article/details/60591881 如侵犯您的版权，请留言回复原文章的地址，我们会给您删除此文章，给您带来不便请您谅解！