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 Izv. IMI UdGU, 2021, Volume 57, Pages 142–155 (Mi iimi413)

MATHEMATICS

Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons

P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov

N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia

Abstract: The problem of finding the optimal location of moving bodies in three-dimensional Euclidean space is considered. We study the problem of finding such a position for two given polytopes $A$ and $B$ at which the Hausdorff distance between them would be minimal. To solve it, the apparatus of convex and nonsmooth analysis is used, as well as methods of computational geometry. Iterative algorithms have been developed and justification has been made for the correctness of their work. A software package has been created, its work is illustrated with specific examples.

Keywords: Hausdorff distance, minimization, subdifferential, Chebyshev center.

DOI: https://doi.org/10.35634/2226-3594-2021-57-06

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Bibliographic databases:

UDC: 514.177
MSC: 11K55, 28A78, 46N10

Citation: P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons”, Izv. IMI UdGU, 57 (2021), 142–155

Citation in format AMSBIB
\Bibitem{LebUspUsh21} \by P.~D.~Lebedev, A.~A.~Uspenskii, V.~N.~Ushakov \paper Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons \jour Izv. IMI UdGU \yr 2021 \vol 57 \pages 142--155 \mathnet{http://mi.mathnet.ru/iimi413} \crossref{https://doi.org/10.35634/2226-3594-2021-57-06}