Akgül, M.2019-02-192019-02-1919880894-069X (print)1520-6750 (online)http://hdl.handle.net/11693/49599It is well‐known that any point in a convex polyhedron P can be written as the sum of a convex combination of extreme points of P and a non‐negative linear combination of extreme rays of P. Grötschel, Lovász, and Schrijver gave a polynomial algorithm based on the ellipsoidal method to find such a representation for any x in P when P is bounded. Here we show that their algorithm can be modified and implemented in polynomial time using the projection method or a simplex‐type algorithm : in n(2n + 1) simplex pivots, where n is the dimension of x. Extension to the unbounded case is immediate.EnglishArticle