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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 3, Pages 397–417 (Mi zvmmf166)  

This article is cited in 1 scientific paper (total in 1 paper)

Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies

G. K. Kamenev

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: A duality theory is developed to describe iterative methods for polyhedral approximation of convex bodies. The various types of approximation problems requiring the application of the duality theory are considered. Based on the theory, approximation methods can be designed for bodies with a dual description (in terms of the support/distance function) and methods can be developed that are optimal in terms of dual complexity characteristics of approximating polytopes (vertices/facets). New optimal methods based on the theory are formulated.

Key words: convex body, polyhedral approximation, algorithm, approximation method, optimal methods, complexity bound, duality.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:3, 376–394

Bibliographic databases:

UDC: 519.658
Received: 02.07.2007

Citation: G. K. Kamenev, “Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies”, Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008), 397–417; Comput. Math. Math. Phys., 48:3 (2008), 376–394

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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