Suppose f is convex on \mathbb{R}^{n}, with domain \text{dom } f. We can make an extended-value extension:
\begin{equation} \tilde{f} \left(x\right) = \begin{cases} f\left(x\right), x \in \text{dom }f \\ \infty, \text{ otherwise } \end{cases} \end{equation}
This could simplify notation .