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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 10, Pages 1668–1678
DOI: https://doi.org/10.7868/S0044466913100050 (Mi zvmmf9930) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Method for finding an approximate solution of the asphericity problem for a convex body

S. I. Dudov, E. A. Meshcheryakova

Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia
Full-text PDF (231 kB) Citations (4)
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DOI: https://doi.org/10.7868/S0044466913100050
Abstract: Given a convex body, the finite-dimensional problem is considered of minimizing the ratio of its circumradius to its inradius (in an arbitrary norm) by choosing a common center of the circumscribed and inscribed balls. An approach is described for obtaining an approximate solution of the problem, whose accuracy depends on the error of a preliminary polyhedral approximation of the convex body and the unit ball of the used norm. The main result consists of developing and justifying a method for finding an approximate solution with every step involving the construction of supporting hyperplanes of the convex body and the unit ball of the used norm at some marginal points and the solution of a linear programming problem.
Key words: asphericity, convex body, approximate solution method, polyhedral approximation, distance function of the nearest and farthest points of a set.
Received: 19.04.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 10, Pages 1483–1493
DOI: https://doi.org/10.1134/S0965542513100059
Bibliographic databases:
Document Type: Article
UDC: 519.65
Language: Russian
Citation: S. I. Dudov, E. A. Meshcheryakova, “Method for finding an approximate solution of the asphericity problem for a convex body”, Zh. Vychisl. Mat. Mat. Fiz., 53:10 (2013), 1668–1678; Comput. Math. Math. Phys., 53:10 (2013), 1483–1493
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
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