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A review of LU factorisation in the simplex algorithm

Author

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  • Joseph M. Elble
  • Nikolaos V. Sahinidis

Abstract

This paper reviews the computational aspects of the LU factorisation of large-scale linear optimisation bases. In the simplex algorithm, the solution of two linear systems, involving a square basis matrix and its transpose, accounts for a large portion of the computation time. The most widely used solution technique is LU factorisation and accompanying update routines. The utilisation of a column replacement update procedure means that a given factorisation may be kept over a large number of simplex iterations. Therefore, a significant emphasis is placed on the sparsity of the LU factors. This emphasis means that a suitable factorisation routine must be chosen with care. A review of LU factorisation is offered, including stability monitoring and analysis, sparsity analysis, error analysis, algorithmic aspects, and state-of-the-art LU factorisation routines.

Suggested Citation

  • Joseph M. Elble & Nikolaos V. Sahinidis, 2012. "A review of LU factorisation in the simplex algorithm," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(4), pages 319-365.
    • Handle: RePEc:ids:ijmore:v:4:y:2012:i:4:p:319-365
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