函数的凸性及其应用

函数的凸性及其应用

摘要

凸性是1种重要的几何性质，凸函数是1类具有特殊性质的函数，本文主要是通过凸函数的1些定义
和定理，来研究它在不等式的证明以及在多元凸函数中找最优解的应用等．首先是借助于凸集引入凸函数的概念，介绍了凸函数的基本性质，并且进1步推出了严格凸函数的1些性质定理．利用函数的凸性可以使不等式证明过程简化，它同时还可以在其它方面有着不容忽视的作用，读者可以从本文的第2部分中充分的感受到．
关键词：凸函数;凸集;凸性

Convexity of function and its application

ABSTRACT

  Convexity is an important geometric property. The convex function is a kind of function with special properties.
This paper mainly talks about the application of convexity in proving inequalities and multivariable convex
function and in finding the best answer with its definition of convex function and theories and so on. This paper
introduces the definition of convex function by the aid of convex set, and, introduces some foundational properties
of the convex function, and concludes some properties and theories of trick convex function. And then, those
properties are important in proving inequalities because they can give the simpler ways, the reader can get benefits
from the examples in the second part of this paper.
Key words  convex function; convexity; convex set