Convex Function Definition A convex function has a very distinct ‘smiley face’ appearance. A line drawn between any two points on the interval will never dip below the graph. It’s more precisely defined as a function where, for every interval on its domain, the midpoint isn’t larger th...
Convex Function 1. Definition $f:\mathbb{R^n} \rightarrow \mathbb{R}$ 是凸函数,且$dom\ f $是凸集,如果 $$ f(\theta x + (1-\theta)y) \leq \theta f(x) + (1-\theta)f(y),\ \forall x,y \in \boldsymbol{dom} f $$ 则称$f$是其定义域上的凸函数。如果$\leq$为$\lt$ ...
发现了一篇介绍convex function的很好的note,将其中要点记录于此。 https://wiki.math.ntnu.no/_media/tma4180/2016v/note2.pdfconvex function definitiondifferentiable propertyHessians property特别值得注意…
1 a :curved or rounded outward like the exterior of a sphere or circle b :being a continuous function or part of a continuous function with the property that a line joining any two points on its graph lies on or above the graph
Define convex. convex synonyms, convex pronunciation, convex translation, English dictionary definition of convex. convex left to right: biconvex, plano-convex, and convexo-concave lenses adj. Having a surface or boundary that curves or bulges outward, a
Convex set and convex function 凸集 定义 给定一个集合\(C \subseteq {R^n}\),满足下列条件则称为凸集 \(x,y \in C \Rightarrow tx + (1 - t)y \in C\),对于任意的\(0 \le t \le 1\) 。 从定义出发,我们也能知道非凸集的情况,下图左侧为凸集,右图为非凸集。
Convex functions basic properties and examples operations that preserve convexity the conjugate function quasiconvex functions log-concave and log-convex functions convexity with respect to generalized inequalities3–1Definitionf : Rn→ R is convex if domf is a convex set and f(θx + (1 θ)y) ...
This chapter presents various results concerning convex functions. Convex functions are very important in the theory of inequalities. The definition of a convex function has a very natural generalization to real-valued function defined on an arbitrary real linear space L. This subject receives full ...
A concave function The problem here is that my original definition of a convex function is also true, I can trace a line between two points of the function without crossing the line... So the mathematicians have been a little bit more specific, and they say that: ...
Definition 定义 domfdomf意思是ff的 domain (定义域) 也就是说其定义域要是一个凸集 Examples on R 一些例子 Examples onRnRnandRm×nRm×n 最后一个是矩阵的最大奇异值(不是一个简单的函数),是凸的。 Restriction of a convex function to a line ...