Li Xin Cheng,Yan Mei Teng.Certain Subsets on Which Every Bounded Convex Function Is Continuous[J]. Acta Mathematica Sinica, English Series .2007(6)Cheng, L. X., Teng, Y. M.: Certain subsets on which every bounde
In this paper, we obtain that eachg-convex function is continuous and convex, and we also extend Jia and Peng’s result on the characterization ofg-convex function without the bounded assumption of the value ofgat the origin.
convex adjective con·vexkän-ˈveks ˈkän-ˌveks kən-ˈveks Synonyms ofconvex 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 ...
1. 凸函数 经济学专有名词 中英对照_百度文库 ... convex: 凸convex function:凸函数convex preference: 凸偏好 ... wenku.baidu.com|基于298个网页 2. 上凸函数 上凸函数,conv... ... ) convex function 凸函数 )convex function上凸函数) convex upper-continuous mapping 上半连续凸函数 ... ...
1.Strong E-convex set,strong E-convex function and strong E-convex programming;强E-凸集,强E-凸函数和强E-凸规划 2.On level sets of E-convex function and E-quasiconvex function有关E-凸函数和E-拟凸函数的水平集 6)convex function凸函数 1.The conditions for n variables continuous function of...
How do we know if a function is convex? The definition with the epigraph is simple to understand, but with functions with several variables it is kind of hard to visualize. So we need to study the function: More generally, a continuous, twice differentiable function of several variables iscon...
f:\R^n\rightarrow \R is convex and f\in C^1 \parallel \nabla f(x)-\nabla f(y)\parallel\leq L\parallel x-y\parallel Lemma for continuous function Suppose f\in C^1 If \parallel \nabla f(x)-\nabla f(y)\parallel\leq L \parallel x-y\parallel then f(y)\leq f(x)+<\nabla...
By Theorem 1.18, f, a proper convex function, is necessarily continuous on ri dom f. As is seen from this theorem, a convex function is continuous in dom f and may have a point of discontinuity only in its boundary. In order to characterize the case in which there is no such ...
Next we consider a point. Infer from the monotonicity ofthat, where the last inequality is ensured by (1.2). Just as for, we see that, whence in view ofwe have that Multiplication with the negative differencegivesfor all. Sincefis continuous, taking the limitfinally shows thatfis non-increa...
Then, f is called convex (respectively, strictly convex) if f(γx,y(t)) is a convex (respectively, strictly convex) function of the time parameter t, for all x, y∈ A. Further, if there exists α > 0 such that f(γx,y(t)) is an α-strongly convex function of t, for all ...