Let us have a set of $n$ points, $x_1, x_2, \ldots, x_n \in \mathbb{R}^d$, that form a convex polytope. And let us have a single point $x \in \mathbb{R}^d$ that is outside of the polytope. How can I compute the $l_1$ distance of the point to the polytope?
I wanted to do it similar to $l_2$ distance. That is, I check the distance for each line segment. Then I find the $l_2$ distance of a line segment to the point and get the minimum among the line segments. It can be done since I can find the smallest distance by using derivation. But, how to do it for $l_1$ distance?