# Definition:Epigraph

Let $f: S \to \overline \R$ be an extended real-valued function.
The epigraph of $f$ is the set:
$\operatorname {epi} \left({f}\right) := \left\{{\left({x, \alpha}\right) \in S \times \R: \ f \left({x}\right) \le \alpha} \right\}$