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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 990–998 (Mi zvmmf4574)  

This article is cited in 5 scientific papers (total in 5 papers)

The modified method of refined bounds for polyhedral approximation of convex polytopes

A. V. Lotova, A. I. Pospelovb

a Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Institute for System Programming, Russian Academy of Sciences, ul. Bol'shaya Kommunisticheskaya 25, Moscow, 109004, Russia

Abstract: The modified method of refined bounds is proposed and experimentally studied. This method is designed to iteratively approximate convex multidimensional polytopes with a large number of vertices. Approximation is realized by a sequence of convex polytopes with a relatively small but gradually increasing number of vertices. The results of an experimental comparison between the modified and the original methods of refined bounds are presented. The latter was designed for the polyhedral approximation of multidimensional convex compact bodies of general type.

Key words: polyhedral approximation of convex bodies, convex polytopes, iterative methods, convergence rate.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 933–941

Bibliographic databases:

UDC: 519.658
Received: 12.10.2007

Citation: A. V. Lotov, A. I. Pospelov, “The modified method of refined bounds for polyhedral approximation of convex polytopes”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 990–998; Comput. Math. Math. Phys., 48:6 (2008), 933–941

Citation in format AMSBIB
\by A.~V.~Lotov, A.~I.~Pospelov
\paper The modified method of refined bounds for polyhedral approximation of convex polytopes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 6
\pages 990--998
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 6
\pages 933--941

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    This publication is cited in the following articles:
    1. G. K. Kamenev, A. I. Pospelov, “Polyhedral approximation of convex compact bodies by filling methods”, Comput. Math. Math. Phys., 52:5 (2012), 680–690  mathnet  crossref  mathscinet  isi  elib  elib
    2. Yu. G. Evtushenko, M. A. Posypkin, L. A. Rybak, A. V. Turkin, “Finding sets of solutions to systems of nonlinear inequalities”, Comput. Math. Math. Phys., 57:8 (2017), 1241–1247  mathnet  crossref  crossref  isi  elib
    3. Evtushenko Yu. Posypkin M. Rybak L. Turkin A., “Approximating a Solution Set of Nonlinear Inequalities”, J. Glob. Optim., 71:1, SI (2018), 129–145  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. Bogomolov S., Forets M., Frehse G., Viry F., Podelski A., Schilling Ch., “Reach Set Approximation Through Decomposition With Low-Dimensional Sets and High-Dimensional Matrices”, Hscc 2018: Proceedings of the 21St International Conference on Hybrid Systems: Computation and Control (Part of Cps Week), Assoc Computing Machinery, 2018, 41–50  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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