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The factorization approach to large-scale linear programming

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Abstract

A unifying concept for large-scale linear programming is developed. This approach, calledfactorization, allows one to isolate the effect of different types of constraints and variables in the algebraic representation of the tableau. Two different factorizations based on a double representation of the tableau are developed. These factorizations are applied to obtain the essential structure of efficient algorithms for generalized upper bounding, coupled block-diagonal problems, set partitioning LPs, minimum cost network flows, and other classes of problems.

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Authors and Affiliations

  1. University of California, Los Angeles, Calif., USA

    G. W. Graves

  2. University of Southern California, Los Angeles, Calif., USA

    R. D. McBride

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  1. G. W. Graves
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  2. R. D. McBride
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Graves, G.W., McBride, R.D. The factorization approach to large-scale linear programming. Mathematical Programming 10, 91–110 (1976). https://doi.org/10.1007/BF01580655

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