I would like to do the following:
Given the V-description of a convex polytope $P \subset \mathbb{R}^m$, a point $x$ which lies outside the polytope, and a point $y \in P$ which is the closest point to $x$ in $P$, construct a vector $v$ which satisfies
$$ v . p \geq 0 \quad \forall\; p \in P $$ $$ v . x < 0 $$
In other words I'd like to construct a hyperplane separating $P$ and $x$. What is a computationally efficient way of doing this? The dimension $m$ is typically pretty large (around 100), and the number of vertices is also very large.
