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Optimization Letters

, Volume 13, Issue 1, pp 227–234 | Cite as

The Demyanov–Ryabova conjecture is false

  • Vera RoshchinaEmail author
Short Communication

Abstract

It was conjectured by Demyanov and Ryabova (Discrete Contin Dyn Syst 31(4):1273–1292, 2011) that the minimal cycle in the sequence obtained via repeated application of the Demyanov converter to a finite family of polytopes is at most two. We construct a counterexample for which the minimal cycle has length 4.

Keywords

Demyanov–Ryabova conjecture Exhausters Demyanov converter 

Notes

Acknowledgements

The author is grateful to the Australian Research Council for continuing financial support via Projects DE150100240 and DP180100602, also to the MATRIX research institute for organising the recent program in algebraic geometry, approximation and optimisation, which provided a fertile research environment that helped this discovery.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.School of ScienceRMIT UniversityMelbourneAustralia
  3. 3.CIAO, Federation University AustraliaBallaratAustralia

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