Mathematical Programming

, Volume 113, Issue 1, pp 1–14

How good are interior point methods? Klee–Minty cubes tighten iteration-complexity bounds


DOI: 10.1007/s10107-006-0044-x

Cite this article as:
Deza, A., Nematollahi, E. & Terlaky, T. Math. Program. (2008) 113: 1. doi:10.1007/s10107-006-0044-x


By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is \(O(2^{n}n^{\frac{5}{2}})\), we prove that solving this n-dimensional linear optimization problem requires at least 2n−1 iterations.


Linear programming Interior point method Worst-case iteration-complexity 

Mathematics Subject Classification (2000)

Primary 90C05 Secondary 90C51 Secondary 90C27 Secondary 52B12 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Antoine Deza
    • 1
  • Eissa Nematollahi
    • 1
  • Tamás Terlaky
    • 1
  1. 1.Advanced Optimization Laboratory, Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

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