The Demyanov–Ryabova conjecture is false
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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.
KeywordsDemyanov–Ryabova conjecture Exhausters Demyanov converter
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.
- 3.Demyanov, V.F.: Exhausters and convexificators—new tools in nonsmooth analysis. In: Quasidifferentiability and Related Topics, vol. 43 of Nonconvex Optim. Appl., pp. 85–137. Kluwer Acad. Publ., Dordrecht (2000)Google Scholar
- 5.Tyrrell, R., Fellar, R.: Convex analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, N.J. (1970)Google Scholar
- 7.Ziegler, G.M.: Lectures on polytopes, volume 152 of Graduate Texts in Mathematics. Springer, New York (1995)Google Scholar