Definition:Convex Real-Valued Function/Real Vector Space

Definition

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 $\R^{n+1}$.

Sources

• 1970: R. Tyrell Rockafellar: Convex Analysis: $\S 4$: Convex Functions