ExamplesA 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
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。
Is the following function convex or concave?: {eq}y=x^2 {/eq}Lesson Summary Register to view this lesson Are you a student or a teacher? I am a student I am a teacher Recommended Lessons and Courses for You Related Lessons Related Courses Helix Angle | Meaning, Equation & Examples ...
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...
Log-determinant f(X) = \log \det X is concave on \bold{dom} \; f = S^n_{++} Proof for theses examples are written on P73.Sublevel sets The \alpha -sublevel set of a convex function f: \mathbb{R}^n \rightarrow \mathbb{R} is: ...
M. Volle: A formula on the conjugate of the max of a convex function and a concave function, J. Math. Anal. Appl. 220 (1998) 313-321.Volle, M. (1998) A formula on the conjugate of the max of a convex function and a concave function. J. Math. Anal. Appl. 220: pp. 313-321...
A function f:Rn→Rf:Rn→R is called quasiconvex if its domain and all its sublevel setsSα={x∈dom f | f(x)≤α}Sα={x∈dom f | f(x)≤α}for all α∈Rα∈R, are convex. A function is quasiconcave if −f−f is quasiconvex, i.e., every superlevel set {x |...
Examples are automatically compiled from online sources to show current usage.Opinions expressed in the examples do not represent those of Merriam-Webster or its editors.Send us feedback. Theconvex& concave mirrors forming the book jacket exaggerate expressions, making others appear stretched, squished...
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...
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 + ...