Epigraph

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Another reference would be good

Definition

Let [ilmath]S\in\mathcal{P}(\mathbb{R}^n)[/ilmath] be an arbitrary subset of [ilmath]\mathbb{R}^n[/ilmath] and let [ilmath]f:S\rightarrow\mathbb{R} [/ilmath] be a function, the epigraph of [ilmath]f[/ilmath], [ilmath]G\subseteq\mathcal{P}(\mathbb{R}^{n+1})[/ilmath] is defined as followsTemplate:RAFCIRAMP:

• [ilmath]G:\eq\{ (x_1,\ldots,x_n,y)\in\mathbb{R}^{n+1}\ \vert\ x\in S\wedge y\eq f(x)\} [/ilmath]

See also

• A function is convex if and only if its domain is convex and its epigraph are convex sets