Mathematical Programming

, Volume 27, Issue 3, pp 241-262

First online:

On the average number of steps of the simplex method of linear programming

  • Steve SmaleAffiliated withDepartment of Mathematics, University of California

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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.

Key Words

Linear Programming Simplex Method Complexity Theory Algorithms Linear Complementarity Problem Path Following