那么我们来讲凸函数（convex function）为什么叫做是凸（convex）的： 这是因为凸函数与凸集（convex set）有联系，而凸集的定义没有争议。 1. 凸函数与凸集通过 sublevel sets 这个概念 …

Aug 16, 2019 · But if I have to check if a given function is convex or not, this definition seems hard and impractical to use. So, my question is, is there any easier way of checking convexity of a …

Oct 22, 2024 · A function is convex if every point on the graph has a supporting line touching it. If the function is differentiable at a point , the supporting line is unique and I equal to the tangent …

Aug 2, 2022 · I have trouble proving that $f (x,y)= x^2 +y^2$ is a convex function with the definition. I know that sum of convex functions is a convex function. But, I am confused ...

@Lost1, there are actually four such rules, for each combination of convex/concave inner and outer functions: convex-nondecreasing & convex -> convex, convex-nonincreasing & concave …

Mar 27, 2015 · The function $g (x)$ is a concave. You can see from your graph that the line passing through two given points on the curve lies below the graph of $g$, not above the …

Besides using the (zero-th order) definition of function convexity (chord is above graph), we can prove the convexity of its epigraph S, which is iff condition of function convexity.

Further comment on the intuition of convexity was given by Raskolnikov, who said Replace the inequality by an equality and you get a linear function. Thus, you could say that convexity is a …

The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective …

Sep 26, 2014 · A convex function is differentiable at all but countably many points Ask Question Asked 11 years, 1 month ago Modified 3 years, 4 months ago