Abstract
The goal is to give some theoretical explanation for the efficiency of the simplex method of George Dantzig. Fixing the number of constraints and using Dantzig's self-dual parametric algorithm, we show that the number of pivots required to solve a linear programming problem grows in proportion to the number of variables on the average.
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Supported in part by NSF Grant #MCS-8102262.
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Smale, S. On the average number of steps of the simplex method of linear programming. Mathematical Programming 27, 241–262 (1983). https://doi.org/10.1007/BF02591902
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DOI: https://doi.org/10.1007/BF02591902