### Projecting a Polytope

Posted:

**Fri Apr 13, 2018 10:20 pm UTC**I'm having some trouble finding a good way to project a convex polytope into lower dimensions. Specifically, I am given a matrix "G" and column vector "h" which define a set of x in R

Note: For two vectors "a" and "b" in R

^{N}such that Gx≤h, and a linear mapping y=Cx. The goal is to find a "P" and "q" to represent Cx as the set of all y such that Py≤q. It's easy to show that P=GC^{-1}and q=h solve the problem if C is invertible, but this doesn't work if y has a lower number of dimensions than x. I could just project each vertex individually if I knew the set of vertices beforehand, but I'm worried that the curse of dimensionality might make it difficult to enumerate the vertices for N on the order of hundreds or even thousands.Note: For two vectors "a" and "b" in R

^{N}, a≤b is equivalent to a(i)≤b(i) for all i=1,...,N.