Geodesic
On a~approximate solution of the problem of aspherical convex compact set
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 4, pp. 13-17.

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

We examine a finite-dimensional problem of minimizing the ratio radius of the ball given a compact convex set (in an arbitrary norm) to the radius of the inscribed sphere through the choice of a common center of these balls. The article offers an approach to building the numerical method of its solution. At each step of the iterative process it is required to solve the problem of convex programming, target function of which is the difference between the radius of a circumscribed sphere, and scalable, with some positive factor, the radius of the inscribed sphere. It is shown that this auxiliary problem, in case of convex compact, and the ball of the used norm being polyhedral, can be reduced to a linear programming problem. 
@article{ISU_2010_10_4_a1,
     author = {S. I. Dudov and E. A. Mesheryakova},
     title = {On a~approximate solution of the problem of aspherical convex compact set},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {13--17},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2010_10_4_a1/}
}
TY  - JOUR
AU  - S. I. Dudov
AU  - E. A. Mesheryakova
TI  - On a~approximate solution of the problem of aspherical convex compact set
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2010
SP  - 13
EP  - 17
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2010_10_4_a1/
LA  - ru
ID  - ISU_2010_10_4_a1
ER  - 
%0 Journal Article
%A S. I. Dudov
%A E. A. Mesheryakova
%T On a~approximate solution of the problem of aspherical convex compact set
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2010
%P 13-17
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2010_10_4_a1/
%G ru
%F ISU_2010_10_4_a1
S. I. Dudov; E. A. Mesheryakova. On a~approximate solution of the problem of aspherical convex compact set. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 4, pp. 13-17. http://geodesic.mathdoc.fr/item/ISU_2010_10_4_a1/

[1] Pshenichnyi B. N., Vypuklyi analiz i ekstremalnye zadachi, Nauka, M., 1980 | MR | Zbl

[2] Dudov S. I., Zlatorunskaya I. V., “Ravnomernaya otsenka vypuklogo kompakta sharom proizvolnoi normy”, Mat. sb., 191:10 (2000), 13–38 | DOI | MR | Zbl

[3] Kamenev G. K., “Skorost skhodimosti adaptivnykh metodov poliedromnoi approksimatsii vypuklykh tel na nachalnom etape”, ZhVM i MF, 48:5 (2008), 763–778 | MR | Zbl

[4] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981 | MR

[5] Demyanov V. F., Rubinov A.M., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990 | MR

[6] Mescheryakova E. A., “O dvukh zadachakh po otsenke vypuklogo kompakta sharom”, Matematika. Mekhanika. Sb. nauch. tr., 10, Izd-vo Sarat. un-ta, Saratov, 2008, 48–50

[7] Dudov S. I. Mescheryakova E. A., “Ob asferichnosti vypuklogo kompakta”, Matematika. Mekhanika. Sb. nauch. tr., 11, Izd-vo Sarat. un-ta, Saratov, 2009, 24–27

[8] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR

[9] Karmanov V. G., Matematicheskoe programmirovanie, Nauka, M., 1986 | MR

[10] Rokafellar R., Vypuklyi analiz, Mir, M., 1973

[11] Zukhovitskii S. I., Avdeeva L. I., Lineinoe i vypukloe programmirovanie, Nauka, M., 1964 | MR

[12] Polovinkin E. S., Balashov M. V., Elementy vypuklogo i silno vypuklogo analiza, Fizmatlit, M., 2004