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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 5, Pages 818–828 (Mi zvmmf9711)  

This article is cited in 3 scientific papers (total in 3 papers)

Polyhedral approximation of convex compact bodies by filling methods

G. K. Kameneva, A. I. Pospelovb

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: A class of iterative methods – filling methods – for polyhedral approximation of convex compact bodies is introduced and studied. In contrast to augmentation methods, the vertices of the approximating polytope can lie not only on the boundary of the body but also inside it. Within the proposed class, Hausdorff or $H$-methods of filling are singled out, for which the convergence rates (asymptotic and at the initial stage of the approximation) are estimated. For the approximation of nonsmooth convex compact bodies, the resulting convergence rate estimates coincide with those for augmentation $H$-methods.

Key words: convex sets, polytopes, iterative algorithms, polyhedral approximation, convergence rate of an algorithm.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:5, 680–690

Bibliographic databases:

UDC: 519.65
Received: 04.05.2011
Revised: 27.11.2011

Citation: G. K. Kamenev, A. I. Pospelov, “Polyhedral approximation of convex compact bodies by filling methods”, Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 818–828; Comput. Math. Math. Phys., 52:5 (2012), 680–690

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Pospelov, “Hausdorff methods for approximating the convex Edgeworth–Pareto hull in integer problems with monotone objectives”, Comput. Math. Math. Phys., 56:8 (2016), 1388–1401  mathnet  crossref  crossref  isi  elib
    2. Shao L., Zhao F., Cong Yu., “Approximation of Convex Bodies By Multiple Objective Optimization and An Application in Reachable Sets”, Optimization, 67:6 (2018), 783–796  crossref  mathscinet  zmath  isi  scopus
    3. V. A. Klyachin, “Approximation of the gradient of a function on the basis of a special class of triangulations”, Izv. Math., 82:6 (2018), 1136–1147  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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