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Steepest Edge as Applied to the Standard Simplex Method

Gavriel Yarmish (yarmish***at***sci.brooklyn.cuny.edu)

Abstract: In this paper we discuss results and advantages of using steepest edge column choice rules and their derivatives. We show empirically, when we utilize the steepest edge column choice rule for the tableau method, that the density crossover point at which the tableau method is more efficient than the revised method drops to 5%. This is much lower than the 72% we have seen when the tableau method used the classical column choice rule. This is due to the fact that the revised method loses much of its gain in terms of lower iteration count do the extra computation necessary in applying steepest edge rules. His can also be seen via a theoretical analysis.

Keywords: Steepest edge, simplex method, Linear Programming, tableau, standard, column choice rules, distrubuted, parallel

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )


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Entry Submitted: 08/29/2013
Entry Accepted: 09/01/2013
Entry Last Modified: 10/11/2013

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