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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 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
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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.
Received: 02.07.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 3, Pages 376–394
DOI: https://doi.org/10.1007/s11470-008-3005-z
Bibliographic databases:
Document Type: Article
UDC: 519.658
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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