凸函数定义

Convex function definition

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1
本文首先归纳总结了凸函数的几个不同的定义，并说明其等价性。
In the first part of this paper, we gave several different definition of convex functions and equivalent proposition.
2
提出了函数的双参数加权平均的定义，证明了一个凸函数的双参数加权平均不等式，加强和推广了有关文献中的结果。
The two - parameters weighted mean in defined and an inequality for two - parameters weighted mean of convex function is prove, they have generalized and improved the results in literatures.
3
然后利用正切锥方向导数定义一类正切锥F 凸函数类，并给出了（VP）正切锥真有效解的充分性条件；
Then, we define a class of tangent cone F convexity in terms of the tangent cone directional derivative, and prove the sufficient optimality conditions for (VP).

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