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)-\
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: ...
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...
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 ...
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 function f(x)=∑j=1kαjfj(x)f(x)=∑j=1kαjfj(x...
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...
Equivalently, a function : is concave if and only if hypo = () : ()is convex (Proposi- tion 3.7, Exercise 3.125) () (0) + (0) for every 0 (Exercise 4.67) : is at 0 if there exists a convex neighbor- hood of 0 such that for every 12 (1 + (1 )2) (1) + (1 )(2)...
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 + ...
basic properties and examples oerations that preserve convexity the conjugation function quasiconvex functions log-concave and log-convex functions convexity with respect to generalized inequality definition f : Rn→Rf : Rn→R is convex if dom ff is a convex set and f(θx+(1−θ)y)≤θf(...
Convex optimization is the process of minimizing a convex objective function subject to convex constraints or, equivalently, maximizing a concave objective function subject to convex constraints. Points satisfying local optimality conditions can be found efficiently for many convex optimization problems. Becau...