Definition:Epigraph

Definition

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

The epigraph of $f$ is the set:

$\map {\operatorname {epi} } f := \set {\tuple {x, \alpha} \in S \times \R: \map f x \le \alpha}$

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): epigraph
• 2013: Francis Clarke: Functional Analysis, Calculus of Variations and Optimal Control: $2.2$: Extended-valued functions, semicontinuity