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Novel update techniques for the revised simplex method

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  • Qi Huangfu
  • J. Hall

Abstract

This paper introduces three novel techniques for updating the invertible representation of the basis matrix when solving practical sparse linear programming problems using a high performance implementation of the dual revised simplex method, being of particular value when suboptimization is used. Two are variants of the product form update and the other permits multiple Forrest–Tomlin updates to be performed. Computational results show that one of the product form variants is significantly more efficient than the traditional approach, with its performance approaching that of the Forrest–Tomlin update for some problems. The other is less efficient, but valuable in the context of the dual revised simplex method with suboptimization. Results show that the multiple Forrest–Tomlin updates are performed with no loss of serial efficiency. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Qi Huangfu & J. Hall, 2015. "Novel update techniques for the revised simplex method," Computational Optimization and Applications, Springer, vol. 60(3), pages 587-608, April.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:3:p:587-608
    DOI: 10.1007/s10589-014-9689-1
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    References listed on IDEAS

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    1. Miles Lubin & J. Hall & Cosmin Petra & Mihai Anitescu, 2013. "Parallel distributed-memory simplex for large-scale stochastic LP problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 571-596, July.
    2. 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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    Cited by:

    1. Fabio Vitor & Todd Easton, 2018. "The double pivot simplex method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 109-137, February.

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