There is a vector $\pmb{v} \in \mathbb{R}^n$ for which the smallest value is to be assigned to $v_{min} \in \mathbb{R}$. But if the smallest value is less than zero, then $v_{min} = 0$ applies.
This is my attempt to express it mathematically:
$v_{min} = \begin{cases} min\ \pmb{v}, & \text{if }\ \ \ \ \ \ min\ \pmb{v} \geq 0 \\ 0, & \text{else} \end{cases}$
Are there alternative or more intuitive mathematical expressions?
You can use something like:$$v_{min}=\max(0,\min{v_i}), v_i\in\mathbb R, i=\overline{1,n}$$In the end it's the same as your definition, just more compact