Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. IMI UdGU:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Full text: PDF file (168 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 514.177
MSC: 11K55, 28A78, 46N10
Received: 01.03.2021

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}


Linking options:
  • http://mi.mathnet.ru/eng/iimi413
  • http://mi.mathnet.ru/eng/iimi/v57/p142

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
    Number of views:
    This page:62
    Full text:13

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021