Definition:Epigraph

Definition
Let $f: S \to \R \cup \left\{{+\infty, -\infty}\right\}$ be an extended-real-valued function.

The epigraph of $f$ is the set:


 * $\operatorname {epi} \left({f}\right) := \left\{ \left({x, \alpha}\right) \in S \times \R: \ f \left({x}\right) \le \alpha \right\}$