Category:Convex Real Function is Pointwise Supremum of Affine Functions

Let $f : \R \to \R$ be a convex real function.

Then there exists a set $\mathcal S \subseteq \R^2$ such that:

$\ds \map f x = \sup_{\tuple {a, b} \in \mathcal S} \paren {a x + b}$

for each $x \in \R$.

Pages in category "Convex Real Function is Pointwise Supremum of Affine Functions"

The following 2 pages are in this category, out of 2 total.