Geodesic
On an Approach to Approximate Solving of the Problem for the Best Approximation for Compact Body by a Ball of Fixed Radius
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 267-272.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the problem of the best approximation of a compact body by a fixed radius ball with respect to an arbitrary norm in the Hausdorff metric. This problem is reduced to a linear programming problem in the case, when compact body and ball of the norm are polytops. 
@article{ISU_2014_14_3_a3,
     author = {S. I. Dudov and M. A. Osipcev},
     title = {On an {Approach} to {Approximate} {Solving} of the {Problem} for the {Best} {Approximation} for {Compact} {Body} by a {Ball} of {Fixed} {Radius}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {267--272},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a3/}
}
TY  - JOUR
AU  - S. I. Dudov
AU  - M. A. Osipcev
TI  - On an Approach to Approximate Solving of the Problem for the Best Approximation for Compact Body by a Ball of Fixed Radius
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 267
EP  - 272
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a3/
LA  - ru
ID  - ISU_2014_14_3_a3
ER  - 
%0 Journal Article
%A S. I. Dudov
%A M. A. Osipcev
%T On an Approach to Approximate Solving of the Problem for the Best Approximation for Compact Body by a Ball of Fixed Radius
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 267-272
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a3/
%G ru
%F ISU_2014_14_3_a3
S. I. Dudov; M. A. Osipcev. On an Approach to Approximate Solving of the Problem for the Best Approximation for Compact Body by a Ball of Fixed Radius. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 267-272. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a3/

[1] Nilol'skii M. S., Silin D. B., “On the best approximation of a convex compact set by elements of addial”, Proc. Steklov Inst. Math., 211, 1995, 306–321 | MR

[2] Dudov S. I., Zlatorunskaya I. V., “Best approximation of compact set by a ball in an arbitrary norm”, Sb. Math., 191:10 (2000), 1433–1458 | DOI | DOI | MR | Zbl

[3] Dudov S. I., “Relations between several problems of estimating convex compacta by balls”, Sb. Math., 198:1 (2007), 43–58 | DOI | DOI | MR | Zbl

[4] Dudov S. I., Meshcheryakova E. A., “Method for finding an approximate solution of the asphericity problem for a convex body”, Comp. Math. and Math. Physics, 53:10 (2013), 1483–1493 | DOI | DOI | Zbl

[5] Pschenichnyi B. N., Convex Analysis and Extremal Problems, Nauka, M., 1980 (in Russian) | MR | Zbl

[6] Dem'yanov V. F., Vasil'ev L. V., Nondifferetiable optimization, Optimization software, Inc., Publications Division, New York, 1985 | MR | MR

[7] Dudov S. I., “Subdifferentiability and superdifferentiability of distance functions”, Math. Notes, 61:4 (1997), 440–450 | DOI | DOI | MR | Zbl

[8] Hiriart-Urruty J. B., “Tangent cones, generalized gradients and mathematical programming in Banach spaces”, Math. Oper. Research, 4:1 (1979), 79–97 | DOI | MR | Zbl

[9] Vasil'ev F. P., Methods of Optimization, MCSMO, M., 2011 (in Russian)

[10] Dudov S. I., Zlatorunskaya I. V., “Best approximation of compact set by a ball in an arbitrary norm”, Adv. Math. Res., 2 (2003), 81–114 | MR | Zbl

[11] Zuhovickij S. I., Avdeeva L. I., Linear and convex programming, Nauka, M., 1964 (in Russian) | MR

[12] Bronstein E. M., “Approximation of convex sets by polytopes”, J. of Math. Sciences, 153:6 (2008), 727–762 | DOI | MR | Zbl