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 bounded convex function is continuous. Acta Mathematica Sinica, English Series , 23...
In this paper, we obtain that each g-convex function is continuous and convex, and we also extend Jia and Peng’s result on the characterization of g-convex function without the bounded assumption of the value of g at the origin. This is a preview of subscription content, log in via an...
More generally, a continuous, twice differentiable function of several variables isconvexon a convex setif and only if its Hessian matrix is positive semidefiniteon the interior of the convex set. (Wikipedia) If we want to check if a function is convex, one easy way is to use our old frien...
If x∈int(dom f),then x is optimal iff x∈D and ∃g∈∂f(x),s.t <g,y−x>≥0,∀y∈D ISTA Consider an imconstrained optimization problem min_{x\in \R^n} F(x)=f(x)+g(x) g \R^n\rightarrow \R is continuous convex function, which is possibly nonsmooth f:\R^n\...
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 ... ...
E-convex functionsE-凸函数 1.Some new properties of their E-convex functions are discussed on the basis of the former researches,and their applications in optimization are researched,some of established Conclusions expanded,these functions perfected.在已有研究基础上,对几类E-凸函数进行了研究,得出了...
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 ...
The righthandside of \left( 0.8 \right) is a a convex quadratic function of \bm{y} (fixed \bm{x}). Setting the gradient with respect to \bm{y} equal to zero, we find then \widetilde{\bm{y}}=\bm{x}-\frac{1}{m}\nabla f\left( \bm{x} \right) minimizes the righthand side...
This was established by Fuglede [13, Theorem 2] provided the domainΩis a Riemannian polyhedron, the targetXis a simply connected complete geodesic NPC metric space, andE:X→Ris a continuous convex function. Recent advances tackled a particular metric spaceXthat does not admit any upper bound ...
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