An asymptotic simplex method for singularly perturbed linear programs

Authors:
Jerzy A. Filar;Eitan Altman;Konstantin E. Avrachenkov
Affiliations:
Centre for Industrial and Applicable Mathematics, School of Mathematics, University of South Australia, The Levels, SA 5095, Australia;INRIA, 2004 Route des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France;INRIA, 2004 Route des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France
Venue:
Operations Research Letters
Year:
2002

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Abstract

We study singularly perturbed linear programs. These are linear programs whose constraints and objective coefficients depend on a small perturbation parameter, and furthermore the constraints become linearly dependent when the perturbation parameter goes to zero. Problems like that were studied by Jeroslow in 1970s. He proposed simplex-like method, which works over the field of rational functions. Here we develop an alternative asymptotic simplex method based on Laurent series expansions. This approach appears to be more computationally efficient. In addition, we point out several possible generalizations of our method and provide simple updating formulae for the perturbed solution.