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A practicable steepest-edge simplex algorithm

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Abstract

It is shown that suitable recurrences may be used in order to implement in practice the steepest-edge simplex linear programming algorithm. In this algorithm each iteration is along an edge of the polytope of feasible solutions on which the objective function decreases most rapidly with respect to distance in the space of all the variables. Results of computer comparisons on medium-scale problems indicate that the resulting algorithm requires less iterations but about the same overall time as the algorithm of Harris [8], which may be regarded as approximating the steepest-edge algorithm. Both show a worthwhile advantage over the standard algorithm.

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Authors and Affiliations

  1. The City College of The City University of New York, New York, USA

    D. Goldfarb

  2. A.E.R.E., Harwell, Oxon, Great Britain

    J. K. Reid

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  1. D. Goldfarb
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  2. J. K. Reid
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Goldfarb, D., Reid, J.K. A practicable steepest-edge simplex algorithm. Mathematical Programming 12, 361–371 (1977). https://doi.org/10.1007/BF01593804

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