Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Hirsch conjecture

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_420

This conjecture is a long-standing one in linear programming and concerns how many simplex iterations (basis changes) are necessary in going from one extreme point to another. Specifically, for any linear-programming problem, does there exist a sequence of m or fewer simplex iterations, each generating a new basic feasible solution, which starts with a given basic feasible solution and ends with some other given basic feasible solution, where m is the number of equations (constraints) in the linear-programming problem? If the conjecture is true, then the optimal solution to the problem could be found in m or less simplex iterations.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA