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。
对应的,我们还有定义“凹函数”(concave function),当 −f 是凸函数时,f 被称为凹函数。 对于仿射函数,它是既凸又凹的。同时,既凸又凹的函数只有仿射函数。 如果f 是凸函数,那么 g(t)=f(x+tv) 也是凸函数,反过来的结论也成立。这说明,凸函数限制在任何一条直线上都是凸的! 凸函数的概念完全可以从欧...
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 ...
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)≤...
Since a function ƒ is concave if and only if − ƒ is convex, any result related to a convex function can easily be translated for a concave function. For this reason only the proofs related to convex functions are presented. For the sake of completeness, the corresponding results for...
Convex & Concave Function Jensen's Inequality Differentiable Convex Function Sufficient & Necessary Conditions for Global Optima Quasiconvex & Quasiconcave functions Differentiable Quasiconvex Function Strictly Quasiconvex Function Strongly Quasiconvex Function Pseudoconvex Function Convex Programming Problem Fritz-...
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...
凹凸棒产品功能(Functionofconcaveandconvexbar)FunctionofconcaveandconvexbarAttapulgite:akindofclaymineralwhichismainlycomposedofAttapulgite.Itisacrystallinehydratedmagnesiumaluminumsilicateminerals,hasauniquelayerchainstructurecharacteristics,thestructureoflatticereplacement,itcontainsnoquantitativecrystalintheNa+,Ca2+,Fe3+...
5) Schur convex(concave)function Schur-凸(凹)函数 6) concavity of function 函数凹凸性 例句>> 补充资料:高斯函数模拟斯莱特函数 尽管斯莱特函数作为基函数在原子和分子的自洽场(SCF)计算中表现良好,但在较大分子的SCF计算中,多中心双电子积分计算极为复杂和耗时。使用高斯函数(GTO)则可使计算大大简化,但高斯...
I.e., basically, a convex function has its curve opening upward like a cup. Whereas a concave function has its curve opening downward like a hat or cap. Convex functions are also called concave upward. A function which is convex cannot have a line segment drawn between two points that is...