Encyclopedia of Operations Research and Management Science

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

Klee-minty problem

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_499
The Klee-Minty problem is a linear-programming problem designed to demonstrate that a problem exists that would require the simplex algorithm to generate all extreme point solutions before finding the optimal. This problem demonstrated that, although the simplex algorithm (under a nondegeneracy assumption) would find an optimal solution in a finite number of iterations, the number of iterations can increase exponentially. Thus, the simplex method is not a polynomially bounded algorithm. One form of the Klee-Minty problem, which defines a slightly perturbed hypercube, is the following:
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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