Polyhedral Computation

Polyhedral Computation

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Many polytopes of practical interest have enormous output complexity and are often highly degenerate, posing severe difficulties for known general-purpose algorithms. They are, however, highly structured, and attention has turned to exploiting this structure, particularly symmetry. Initial applications of this approach have permitted computations previously far out of reach, but much remains to be understood and validated experimentally. The papers in this volume give a good snapshot of the ideas discussed at a Workshop on Polyhedral Computation held at the CRM in Montreal in October 2006 and, with one exception, the current state of affairs in this area. The exception is the inclusion of an often cited 1980 technical report of Norman Zadeh, which was never published in a journal and has passed into the folklore of the discipline. This paper illustrates beautifully the work still to be done in the field: it gives a simple pivot rule for the simplex method for which it is still unknown if it yields a polynomial time algorithm.For example, we and consider the closure of its conic hull. ... For example, if v1 , ... , v n aˆˆ Rd span a k-dimensional linear subspace, we may just choose (project onto) k independent coordinates. The appropriate projection (i.e. equations of the linearity space) can be found efficiently via Gaussian elimination. In other ... A face of P is a set {xaˆˆP: f(x)=0} where f is an element of Paˆ— = {f aˆˆ (Rd)aˆ— : f(x) a‰y 0 for all x aˆˆP}, the polyhedral cone dual to P.Notethat(Paˆ—)aˆ— = P. The faces of a pointedanbsp;...

Title:Polyhedral Computation
Author:David Avis, David Bremner, Antoine Deza
Publisher:American Mathematical Soc. - 2009


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