Geodesic
Polyhedral approximation of convex compact bodies by filling methods
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 818-828 
G. K. Kamenev; A. I. Pospelov. Polyhedral approximation of convex compact bodies by filling methods. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 818-828. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A class of iterative methods – filling methods – for polyhedral approximation of convex compact bodies is introduced and studied. In contrast to augmentation methods, the vertices of the approximating polytope can lie not only on the boundary of the body but also inside it. Within the proposed class, Hausdorff or $H$-methods of filling are singled out, for which the convergence rates (asymptotic and at the initial stage of the approximation) are estimated. For the approximation of nonsmooth convex compact bodies, the resulting convergence rate estimates coincide with those for augmentation $H$-methods.

[1] Bronshtein E. M., “Approksimatsiya vypuklykh mnozhestv mnogogrannikami”, Sovremennaya matem. Fundamentalnye napravleniya. Geometriya, 22, RUDN, M., 2007, 5–37 | MR

[2] Gruber P. M., “Aspects of approximation of convex bodies”, Handbook of Convex Geometry, eds. P. M. Gruber, J. M. Wills, Elsevier Sci. Publishers B. V., 1993, 321–345 | MR

[3] Lotov A. V., Bushenkov V. A., Kamenev G. K., Chernykh O. L., Kompyuter i poisk kompromissa. Metod dostizhimykh tselei, Nauka, M., 1997

[4] Lotov A. V., Bushenkov V. A., Kamenev G. K., Interactive decision maps. Approximation and visualization of Pareto frontier, Kluwer Academic Publishers, Boston, 2004 | MR | Zbl

[5] Kamenev G. K., Optimalnye adaptivnye metody poliedralnoi approksimatsii vypuklykh tel, VTs RAN, M., 2007 | MR

[6] Kamenev G. K., “Ob odnom klasse adaptivnykh algoritmov approksimatsii vypuklykh tel mnogogrannikami”, Zh. vychisl. matem. i matem. fiz., 32:1 (1992), 136–152 | MR

[7] Pospelov A. I., “Approksimatsiya vypukloi obolochki Edzhvorta–Pareto v mnogokriterialnykh zadachakh s monotonnymi kriteriyami”, Zh. vychisl. matem. i matem. fiz., 49:10 (2009), 1765–1778 | MR | Zbl

[8] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR

[9] Lotov A. V., Pospelov A. I., “Modifitsirovannyi metod utochneniya otsenok dlya poliedralnoi approksimatsii vypuklykh mnogogrannikov”, Zh. vychisl. matem. i matem. fiz., 48:6 (2008), 990–998 | MR | Zbl

[10] Kamenev G. K., “Ob effektivnosti khausdorfovykh algoritmov poliedralnoi approksimatsii vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 33:5 (1993), 796–805 | MR | Zbl