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] ...
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) ...
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)≤...
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 ...
网络凹凸函数 网络释义 1. 凹凸函数 伪凹函数,pseudoconcave... ... ) upper convex function 上凹函数 )convex and concave functions凹凸函数... www.dictall.com|基于 1 个网页
1) convex and concave functions 凸函数和凹函数 2) E-convex function E-凸函数 1. Strong E-convex set,strongE-convex functionand strong E-convex programming; 强E-凸集,强E-凸函数和强E-凸规划 2. E-convex functionis the generation of convex function,i. ...
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,to convex and concave functions. 将一维随机变量...
A class of k-log-convex functions and their applications to some special functions Let a and b be two real numbers and f be a positive and differentiable function on an interval I. The authors establish the i-log-convex or i-log-concave p... F Qi,S Guo,BN Guo,... - 《Integral ...
Lecture notes based on c2001 Michael Carter All rights reservedConcave and convex functions: is if for every 12 in (1 + (1 )2) (1) + (1 )(2) for every 0 1 It is if the inequality is strict, and if the inequality is reversed. Equivalently, a function : is concave if and only...