Mathematical Programming

, Volume 27, Issue 3, pp 241–262

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

  • Steve Smale
Article

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.

Key Words

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

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Copyright information

© The Mathematical Programming Society, Inc. 1983

Authors and Affiliations

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

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