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, Volume 27, Issue 3, pp 241262
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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 selfdual 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 Title
 On the average number of steps of the simplex method of linear programming
 Journal

Mathematical Programming
Volume 27, Issue 3 , pp 241262
 Cover Date
 198310
 DOI
 10.1007/BF02591902
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Linear Programming
 Simplex Method
 Complexity Theory
 Algorithms
 Linear Complementarity Problem
 Path Following
 Industry Sectors
 Authors

 Steve Smale ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA