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$\lt$ ...
Two common examples are the exponential function y = exp(x) and the square function y = x2.See also concave function.● Classic Economic Models Interactive presentations of the most important models in microeconomics and macroeconomics go beyond anything appearing in a printed-on-paper textbook. ...
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…
Ifu:Ω⊂Rd→Xis a harmonic map valued in a metric spaceXandE:X→Ris a convex function, in the sense that it generates anEVI0-gradient flow, we prove that the pullbackE∘u:Ω→Ris subharmonic. This property was known in the smooth Riemannian manifold setting or with curvature restrictio...
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 ...
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) ...
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
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 ...
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。
The meaning of CONVEX is curved or rounded outward like the exterior of a sphere or circle. How to use convex in a sentence.