On asphericity of convex bodies

The paper deals with a finite-dimensional problem of minimizing the ratio of the radius of the sphere circumscribed about a given convex body (in an arbitrary norm) to the radius of the inscribed sphere. The minimization is performed by choosing a common center of these spheres. We prove that the ob...

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Bibliographic Details
Published inRussian mathematics Vol. 59; no. 2; pp. 36 - 47
Main Authors Dudov, S. I., Meshcheryakova, E. A.
Format Journal Article
LanguageEnglish
Published Heidelberg Allerton Press 01.02.2015
Subjects
Mathematics
Mathematics and Statistics
subdifferential
asphericity
quasiconvexity
convex body
uniform bound
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Summary:The paper deals with a finite-dimensional problem of minimizing the ratio of the radius of the sphere circumscribed about a given convex body (in an arbitrary norm) to the radius of the inscribed sphere. The minimization is performed by choosing a common center of these spheres. We prove that the objective function of this problem is quasiconvex and subdifferentiable and establish a criterion for the unique solvability of the problem. The considered problem is compared with those close to it in geometric sense.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X15020061