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

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, wh...

Full description

Saved in:
Bibliographic Details
Published inComputational mathematics and mathematical physics Vol. 53; no. 10; pp. 1483 - 1493
Main Authors Dudov, S. I., Meshcheryakova, E. A.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.10.2013
Springer Nature B.V
Subjects
Approximation
Asphericity
Computational mathematics
Computational Mathematics and Numerical Analysis
Construction
Hyperplanes
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Norms
Physics
Studies
approximate solution method
asphericity
polyhedral approximation
convex body
distance function of the nearest and farthest points of a set
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542513100059