Convex and Concave Function - Let $f:S rightarrow mathbb{R}$, where S is non empty convex set in $mathbb{R}^n$, then $fleft ( x right )$ is said to be convex on S if $fleft ( lambda x_1+left ( 1-lambda right )x_2 right )leq lambda fleft ( x_1 right )+le
如果作为Rn+1的子集,集合epif是凸的,则我们将函数f定义为S上的凸函数。 4.1.3 定义(凹函数)concave function 空间\mathbb{R}^n上的子集S上的函数f是凹函数,当它的相反函数-f是凸函数时,这个函数在子集S上就是凹函数。 也即是,在空间\mathbb{R}^{n+1}中的子集epi(-f)是一个凸集时,函数f就是空间\...
A function f:R^n \to R is logarithmically concave or log-concave if f(x)>0,\forall x\in dom f and \log f is concave,for a log-concave function f,we have f(\theta x+(1-\theta)y)\geq f(x)^\theta f(y)^{1-\theta},\forall x,y\in dom f,\theta \in [0,1] ...
Concave and Convex Function 技术标签:函数mathConcaveConvexmachine-learning 查看原文 多载波MIMO信道下的波束成形设计 whentheweights are in increasing order ,anditisthenaSchur-concavefunctiononeach carrier...isthenaSchur-concavefunction.Theproblem inconvexform (theobjectiveislinearandthe...
The mean value inequality of the power about the convex function (3)\,(4) [1] has been obtained when α≥1 in paper \. This paper points out an error in paper \, It is in this paper that the author obtains the mean value inequality of power about the concave function when α≤1...
函数f(x)f(x)是严格凸(strictly convex)的. 如果−f−f是凸的, 则ff是凹(concave)的. 凸函数如下图所示 2.1 凸函数的一阶条件 如果一个函数f:Rn→Rf:Rn→R是可微的, 那么ff是凸函数当且仅当D(f)D(f)是凸集, 并且对于任意的x,y∈D(f)x,y∈D(f): ...
The current work analyses such performance improvements of convex-concave objective thoroughly. Our study indicates that a KL-Divergence based loss function for semi-supervised learning has performed much better than the convex-concave objective based on L2-Loss. It is also seen that the one-versus...
函数f(x)f(x)是严格凸(strictly convex)的. 如果−f−f是凸的, 则ff是凹(concave)的. 凸函数如下图所示 2.1 凸函数的一阶条件 如果一个函数f:Rn→Rf:Rn→R是可微的, 那么ff是凸函数当且仅当D(f)D(f)是凸集, 并且对于任意的x,y∈D(f)x,y∈D(f): ...
for concave function. However, the usual distinction between the two is that “concave down” refers to theshapeof a graph, or part of a graph. While some functions can have parts that are concave up and other parts that are concave down, a concavefunctionis concave up for itsentiredomain...
concave and convex operators 凹算子与凸算子「阴~皿d阴vex.耳阳.勿韶;.留叮.肠疽“‘.小啊j阅雌口叹甲司 半序空间中的非线性算子,类似于一个实变量的凹函数与凸函数. 一个Banach空间中的在某个锥K上是正的非线性算子A,称为凹的(concave)(更确切地,在K上u。凹的),如果 l)对任何的非零元x任K,...