How to check if a function is convex - Mathematics Stack Exchange
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 …
Intuition behind the definition(s) of a convex function
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 …
Prove $f(x,y)= x^2 + y^2$ is convex function - Mathematics Stack …
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 ...
Is $g (x)=\log x$ convex function? - Mathematics Stack Exchange
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 …
Is $f(x)=|x|$ a convex function? - Mathematics Stack Exchange
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.
The composition of two convex functions is convex
@Lost1, there are actually four such rules, for each combination of convex/concave inner and outer functions: convex-nondecreasing & convex -> convex, convex-nonincreasing & concave …
real analysis - Prove that every convex function is continuous ...
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 …
real analysis - A convex function is differentiable at all but ...
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
How is the function $x \\mapsto x^4$ strictly convex?
A strongly convex function is strictly convex but the converse need not be true. The condition for strict convexity is strict Jensen's inequality as pointed out by Alex R.
Convexity of supremum of convex functions - Mathematics Stack …
Sep 21, 2019 · Convexity of supremum of convex functions Ask Question Asked 6 years, 1 month ago Modified 6 years, 1 month ago