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
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 ...
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…
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) ...
The standard definition of a close-to-convex function involves a complex numerical factor ei尾 which is on occasion erroneously replaced by 1. While it is known to experts in the field that this replacement cannot be made without essentially changing the class, explicit reasons for this fact ...
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
1 凸分析convex analysis
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: ...
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。
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 ...