Category:Definitions/Convex Real-Valued Functions

This category contains definitions related to Convex Real-Valued Functions.
Related results can be found in Category:Convex Real-Valued Functions.

Let $\R^n$ be an $n$-dimensional real vector space.

Let $S \subseteq \R^n$ be a subset.

Let $f: S \to \overline \R$ be an extended real-valued function.

$f$ is convex if and only if its epigraph is a convex subset of $\R^{n+1}$.