Visualizing and Constructing Cycles in the Simplex Method

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Most examples of cycling in the simplex method are given without explanation of how they were constructed. An exception is Beale’s 1955 example built around the geometry of the dual simplex method in the plane. Using this approach we give a simple geometric explanation for a number of examples of cycling in the simplex method, including Alan Hoffman’s original example. This gives rise to a simple method for generating examples with cycles.

, 18 pages

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G-2005-33.pdf (180 Ko)