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The Demyanov–Ryabova conjecture is false

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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.

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

    Vera Roshchina

  2. School of Science, RMIT University, Melbourne, Australia

    Vera Roshchina

  3. CIAO, Federation University Australia, Ballarat, Australia

    Vera Roshchina

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  1. Vera Roshchina
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Correspondence to Vera Roshchina.

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Roshchina, V. The Demyanov–Ryabova conjecture is false. Optim Lett 13, 227–234 (2019). https://doi.org/10.1007/s11590-018-1296-0

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  • DOI: https://doi.org/10.1007/s11590-018-1296-0

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