Given a $n$-dimensional convex polytope defined by $A x\leq b$ and $A_{eq} x = b_{eq}$, is there an efficient way to determine the average coordinates of all vertices without enumerating them? (As if each vertex was a point particle)
I am currently using a vertex enumeration program and then just averaging the results, but that seems a waste of memory - as I only want the average of the points and not the full enumeration as I can have relatively large $n$ and lots of constraints.