Suppose \(f\) is convex on \(\mathbb{R}^{n}\), with domain \(\text{dom } f\). We can make an extended-value extension:

\begin{equation} \tilde{f} \qty(x) = \begin{cases} f\qty(x), x \in \text{dom }f \\ \infty, \text{ otherwise } \end{cases} \end{equation}

This could simplify notation .