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

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

2000-12-22

arxiv.org/abs/math/0012242v1

Mathematics

Optimization and Control

Submitted to Mathematical Programming

Scientific paper

This 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.

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