Abstract
Recently R.G. Bland proposed two new rules for pivot selection in the simplex method. These elegant rules arise from Bland’s work on oriented matroids; their virtue is that they never lead to cycling. We investigate the efficiency of the first of them. On randomly generated problems with 50 nonnegative variables and 50 additional inequalities, Bland’s rule requires about 400 iterations on the average; the corresponding figure for the popular “largest coefficient” rule is only about 100. Comparable behaviour seems to persist even on highly degenerate problems. On the theoretical side, we analyse the performance of Bland’s rule on the classical Klee-Minty examples: for problems with n nonnegative variables and n additional inequalities, the number of iterations is bounded from below by the n-th Fibonacci number.
This research was supported by NRC grant A9211.
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© 1978 The Mathematical Programming Society
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Avis, D., Chvátal, V. (1978). Notes on Bland’s pivoting rule. In: Balinski, M.L., Hoffman, A.J. (eds) Polyhedral Combinatorics. Mathematical Programming Studies, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121192
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DOI: https://doi.org/10.1007/BFb0121192
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