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The Iteration-Complexity Upper Bound for the Mizuno-Todd-Ye Predictor-Corrector Algorithm is Tight

  • Murat MutEmail author
  • Tamás Terlaky
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 279)

Abstract

It is an open question whether there is an interior-point algorithm for linear optimization problems with a lower iteration-complexity than the classical bound \(\mathcal {O}(\sqrt{n} \log (\frac{\mu _1}{\mu _0}))\). This paper provides a negative answer to that question for a variant of the Mizuno-Todd-Ye predictor-corrector algorithm. In fact, we prove that for any \(\varepsilon >0\), there is a redundant Klee-Minty cube for which the aforementioned algorithm requires \(n^{( \frac{1}{2}-\varepsilon )} \) iterations to reduce the barrier parameter by at least a constant. This is provably the first case of an adaptive step interior-point algorithm where the classical iteration-complexity upper bound is shown to be tight.

Keywords

Curvature Central path Polytopes Complexity Interior-point methods Linear optimization 

Mathematics Subject Classification (2000)

65K05 68Q25 90C05 90C51 90C60 

Notes

Acknowledgements

Research supported by a Start-up grant of Lehigh University. It is also supported by TAMOP-4.2.2.A-11/1KONV-2012-0012: Basic research for the development of hybrid and electric vehicles. The TAMOP Project is supported by the European Union and co-financed by the European Regional Development Fund.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringLehigh UniversityBethlehemUSA

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