The function f is said to be strictly convex on S if the above inequality is strict for X1≠ X 2, and 0 < ( < 1. A function f is said to be concave (strictly concave) if –f is convex (strictly convex). It is clear that a linear function is convex as well as concave but ...
log convex function乘积是log convex function 积分,如果f(x,y)是log-convex那么对于\forall y\in C,g(x)=\int_C f(x,y)dy是log-convex的 Integration of log-concave functions log-concave在积分下不能保证log-concave的性质,但是假设f:R^n\times R^m\to R是log-concave的,那么 ...
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\mathbb{R}^n 中的子集S 上的凹函数。
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 ...
Convexandconcavefunctions 2.5.Convex and concave functions Let f be a real-valued function f:S→R.In what follows,we assume that S⊆R n is a convex set.The function f is convex on a set S if∀x1,x2∈S,∀λ∈[0,1]such thatλx1+(1−λ)x2∈S,f(λx1+(1−λ)x2)≤...
A linear function is both convex and concave. f(x)=|x|f(x)=|x| is a convex function. f(x)=1xf(x)=1x is a convex function.TheoremLet f1,f2,...,fk:Rn→Rf1,f2,...,fk:Rn→R be convex functions. Consider the function f(x)=∑j=1kαjfj(x)f(x)=∑j=1kαjfj(x) ...
The conjugate function Examples Quasiconvex functions Examples internal rate of return 内部收益率 Properties Log-concave and log-convex functions 正态分布的密度函数取 log 之后是一个常数减去一个凸的二次函数,因此是 concave 的 老师还讲了在任意集合上的均匀分布都是 log-concave 的,脑补一下,其概率密度...
A function that is convex will have a slope that is increasing. Additionally, all convex functions have only one minimum value. This is because the curve is opening upward, so the very tip of the bottom of the curve is the function's minimum. Concave curves on the other hand open up ...
1) concave (convex) functions 凹(凸)函数 例句>> 2) convex and concave functions 凹凸函数 1. This article popularizes the single-dimensional random variable f≤Ef(ξ)(f(x) as convex and concave function into the multi-dimentional scope;therefore concludes a series of important inequalties esp...
xlogx on R++ concave: affine: ax + b on R, for any a, b ∈ R powers: xαon R++, for 0 ≤α≤ 1 logarithm: logx on R++Convex functions 3–3Examples on Rnand Rm×naffine functions are convex and concave; all norms are convex examples on Rn affine function f(x) = aTx + ...