Abstract
Linear programming in core using a variant of the Bartels-Golub decomposition of the basis matrix will be considered. This variant is particularly well-adapted to sparsity preservation, being capable of revising the factorisation without any fill-in whenever this is possible by permutations alone. In addition strategies for colum pivoting in the simplex method itself will be discussed and in particular it will be shown that the “steepest edge” algorithm is practical. This algorithm has long been known to give good results in respect of number of iterations, but has been thought to be impractical.
Test results on genuine problems with hundreds of rows and thousands of columns will be reported. These tests include comparisons with other methods.
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Reid, J.K. (1976). Sparse in-core linear programming. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080124
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DOI: https://doi.org/10.1007/BFb0080124
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