I have multiple (convex and bounded) polytopes, all of them describing the feasible area of a given LP (the rest of the LP is always the same), for a number of scenarios. Since those polytopes are too complex I'm looking to
(a) simplify them (e.g. transforming a polytope defined by $n$ constraints to one with $m << n$ constraints), and
(b) aggregate them by finding a representative "average" (or "median") polytope.
For (a) I assume that some kind of either "smallest" convex hull, or "largest" convex polytope, with $m$ constraints could work (?).
For (b) I'm kind of lost, on what a reasonable approach would be (side-note: it can be assumed that most of the polytopes to be aggregated overlap, and many also by quite some volume).
Are there any algorithms out there that I could check out? Since I'm dealing with a lot of really high-dimensional polytopes I'm looking for something that works in practice (and not necessarily has to be "exact").