# identifying vertices of a polytope given as a convex hull of points

I have a linear programming problem where the polytope is described as a convex hull of an exponential number ($2^d$) of points in d-dimensional space. What could be an approach? Do you first identify the set of vertices from the $2^d$ points and check which vertex maximizes the objective? Is there an efficient algorithm to identify the set of vertices from the given set of $2^d$ points?

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This might be useful: mathoverflow.net/questions/97131/… –  Yoav Kallus Apr 12 '13 at 22:05