Convex functions are an important content of mathematical analysis, and it is also the focus and difficulty part of teaching. This paper introduces three equivalent definitions of the convex function, and gives some properties of convex functions. Finally, several useful inequalities are also discussed from the perspective of...
I am trying to find the convex hull of a finite set in a hyperbolic space, particularly the Poincare disk, but the Upper Half plane works as well. I know the following equivalent definitions of the Convex Hull: 1) It is the smallest convex set containing the points 2) If the set is....
the topic of minimizing nonsmoothconvex functionsis discussed and the definitions ofsubgradientand subdifferential are provided. The method of subgradient iterative minimization and some of its versions are presented. The regret analysis technique is discussed. The chapter closes with presenting the proximal...
网络释义 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 ......
According to the article 1 ,we will give some definitions ofquasiconvexfunction,and discuss their equivalent. 在文献1的基础上,给出了拟凸函数的几种定义形式,并讨论了它们之间的等价关系。 更多例句>> 6) quasi-convex functions 拟凸函数 1.
(This condition is easily seen to be equivalent to the definition of strict convexity given in 22.38.) (I) || || is a strictly convex function (as defined in 12.17.c) on each straight line that does not pass through 0. In other words, if u and v are points satisfying||λu + (...
ConvexFunction Definition Derivativetests Operationsthatpreserveconvexity Examples QuadraticPrograms + Quickdefinitions Convexset Forallx,yinC:θx+(1-θ)yisinCforθ\in[0,1] Affineset Forallx,yinC:θx+(1-θ)yisinC Allaffinesetsarealsoconvex
Proposition 1.1.2: For a function f : ℜn → [−∞, ∞], the following are equivalent: (i) The level set Vγ = x | f (x) ≤γ is closed for every scalar γ. (ii) f is lower semicontinuous. (iii) epi(f ) is closed. Proposition 1.1.3: Let f : X → [−∞, ∞...
Acronyms [′kän‚veks ′prō‚gram·iŋ] (mathematics) Nonlinear programming in which both the function to be maximized or minimized and the constraints are appropriately chosen convex or concave functions of the independent variables.
Condition (6) can be rewritten in the following equivalent form: Re z f ′ ( z ) F α ( z ) > 0 , z ∈ Δ , (7) where the function F α ( z ) = z 1 − α z 2 = z + ∑ n = 2 ∞ α n z 2 n + 1 , z ∈ Δ is starlike for α ∈ [ − 1 , 1 ...