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 c
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...
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。
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...
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)≤...
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-...
for all α∈Rα∈R, are convex. A function is quasiconcave if −f−f is quasiconvex, i.e., every superlevel set {x | f(x)≥α}{x | f(x)≥α} is convex. A function that is both quasiconvex and quasiconcave is called quasilinear. If a function is quasilinear, then ...
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...
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...
6) concavity of function 函数凹凸性 例句>> 补充资料:凹算子与凸算子 凹算子与凸算子 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...