The simplest examples where the simplex method cycles and conditions where EXPAND fails to prevent cycling

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dc.creatorHall, J. A. J.
dc.creatorMcKinnon, K. I. M.
dc.date2000-12-22
dc.date.accessioned2026-07-07T04:39:24Z
dc.date.available2026-07-07T04:39:24Z
dc.descriptionThis paper introduces a class of linear programming examples which cause the simplex method to cycle indefinitely and which are the simplest possible examples showing this behaviour. The structure of examples from this class repeats after two iterations. Cycling is shown to occur for both the most negative reduced cost and steepest edge column selection criteria. In addition it is shown that the EXPAND anti-cycling procedure of Gill et al.is not guaranteed to prevent cycling.
dc.descriptionSubmitted to Mathematical Programming
dc.identifierhttps://arxiv.org/abs/math/0012242
dc.identifierhttp://arxiv.org/abs/math/0012242
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60646
dc.subjectOptimization and Control
dc.titleThe simplest examples where the simplex method cycles and conditions where EXPAND fails to prevent cycling
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