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Permutations in the Factorization of Simplex Bases

Author

Listed:
  • Ricardo Fukasawa

    (Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

  • Laurent Poirrier

    (Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

Abstract

The basis matrices corresponding to consecutive iterations of the simplex method only differ in a single column. This fact is commonly exploited in current linear programming solvers to avoid having to compute a new factorization of the basis at every iteration. Instead, a previous factorization is updated to reflect the modified column. Several methods are known for performing the update, most prominently the Forrest–Tomlin method. We present an alternative algorithm for the special case where the update can be performed purely by permuting rows and columns of the factors. In our experiments, this occurred for about half of the basis updates, and the new algorithm provides a modest reduction in computation time for the dual simplex method.

Suggested Citation

  • Ricardo Fukasawa & Laurent Poirrier, 2019. "Permutations in the Factorization of Simplex Bases," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 612-632, July.
    • Handle: RePEc:inm:orijoc:v:31:y:2019:i:3:p:612-632
    DOI: 10.1287/ijoc.2018.0862
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    References listed on IDEAS

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    1. Uwe H. Suhl & Leena M. Suhl, 1990. "Computing Sparse LU Factorizations for Large-Scale Linear Programming Bases," INFORMS Journal on Computing, INFORMS, vol. 2(4), pages 325-335, November.
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