f: \mathbb{R}^{n} \to \mathbb{R} is convex IFF the function g: \mathbb{R} \to \mathbb{R} is convex:
\begin{equation} g\left(t\right) = f\left(x + tv\right), \text{dom } g = \left\{t \mid x + tv \in \text{dom }f\right\} \end{equation}
is convex in t \in \mathbb{R} for any x \in \text{dom } f, v \in \mathbb{R}^{n}.