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。
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) ...
log convex function is convex and a nonnegative concave function is log-concave 性质 Log-convex function二次微分 g(x)=\log f(x)\\ \nabla g(x)=\frac{1}{f(x)}\nabla f(x)\\ \nabla^2 g(x)=\frac{1}{f(x)}\nabla^2 f(x)-\frac{1}{f^2(x)}\nabla f(x)\nabla f(x)^T...
Concave and Convex Function What is Concave Function? Concave function is a function where the line segement between any two points of the function lies below or on the graph.[1] Mathematically, as fo...查看原文多载波MIMO信道下的波束成形设计 when the weights are in increasing order , and ...
Aconcave functionhas a distinct arched appearance when graphed: The term concave down is sometimes used as a synonym 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...
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): ...
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): ...
Convex-concave utility functionHartl, Richard FMehlmann, Alexander
Words You Always Have to Look Up How to Use Em Dashes (—), En Dashes (–) , and Hyphens (-) Words in Disguise: Do these seem familiar? Why is '-ed' sometimes pronounced at the end of a word? Democracy or Republic: What's the difference?
Browse Nearby Words convex convexity convexo-concave See all Nearby Words Cite this Entry Style “Convexity.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/convexity. Accessed 7 May. 2025. Copy Citation ...