Mathematical Programming

, Volume 27, Issue 3, pp 241–262

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

  • Steve Smale

DOI: 10.1007/BF02591902

Cite this article as:
Smale, S. Mathematical Programming (1983) 27: 241. doi:10.1007/BF02591902


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 ProgrammingSimplex MethodComplexity TheoryAlgorithmsLinear Complementarity ProblemPath Following

Copyright information

© The Mathematical Programming Society, Inc. 1983

Authors and Affiliations

  • Steve Smale
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA