An algorithmic proof of the polyhedral decomposition theorem

Mustafa Akgül

Naval Research Logistics (NRL), 1988, vol. 35, issue 5, 463-472

Abstract: It 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.

Date: 1988
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https://doi.org/10.1002/1520-6750(198810)35:53.0.CO;2-5

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:35:y:1988:i:5:p:463-472

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