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

Article

- Received:
- Revised:

DOI: 10.1007/BF02591902

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

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## 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## Copyright information

© The Mathematical Programming Society, Inc. 1983