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

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 …

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 ...

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 …

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 …

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 …

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 …

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

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.

Aug 23, 2018 · It follows that any log-convex function is also convex, as the exponential of a convex function. In general nothing can be said about the composition of a concave function …