@article{ZVMMF_2003_43_8_a0,
author = {G. K. Kamenev},
title = {Self-dual adaptive algorithms for polyhedral approximation of convex bodies},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1123--1137},
year = {2003},
volume = {43},
number = {8},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_8_a0/}
}
TY - JOUR AU - G. K. Kamenev TI - Self-dual adaptive algorithms for polyhedral approximation of convex bodies JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2003 SP - 1123 EP - 1137 VL - 43 IS - 8 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_8_a0/ LA - ru ID - ZVMMF_2003_43_8_a0 ER -
G. K. Kamenev. Self-dual adaptive algorithms for polyhedral approximation of convex bodies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 8, pp. 1123-1137. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_8_a0/
[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961
[2] Lotov A. V., Bushenkov V. A., Kamenev G. K., Chernykh O. L., Kompyuter i poisk kompromissa. Metod dostizhimykh tselei, Nauka, M., 1997
[3] Lotov A. V., Bushenkov V. A., Kamenev G. K., Metod dostizhimykh tselei. Matematicheskie osnovy i ekologicheskie prilozheniya, Mellen Press, Lewiston, New York, USA, 1999
[4] Bushenkov V. A., Lotov A. V., Metody postroeniya i ispolzovaniya obobschennykh mnozhestv dostizhimosti, VTs AN SSSR, M., 1982
[5] Kamenev G. K., “Ob odnom klasse adaptivnykh algoritmov approksimatsii vypuklykh tel mnogogrannikami”, Zh. vychisl. matem. i matem. fiz., 32:1 (1992), 136–152 | MR
[6] Kamenev G. K., “Ob effektivnosti khausdorfovykh algoritmov poliedralnoi approksimatsii vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 33:5 (1993), 796–805 | MR | Zbl
[7] Kamenev G. K., “Issledovanie odnogo algoritma approksimatsii vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 34:4 (1994), 608–616 | MR | Zbl
[8] Kamenev G. K., “Effektivnye algoritmy approksimatsii negladkikh vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 39:3 (1999), 446–450 | MR | Zbl
[9] Kamenev G. K., “Sopryazhennye adaptivnye algoritmy poliedralnoi approksimatsii vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 22:9 (2002), 1351–1367 | MR
[10] Kamenev G. K., “Algoritm sblizhayuschikhsya mnogogrannikov”, Zh. vychisl. matem. i matem. fiz., 36:4 (1996), 134–147 | MR | Zbl
[11] Burmistrova L. V., “Issledovanie novogo metoda approksimatsii vypuklykh kompaktnykh tel mnogogrannikami”, Zh. vychisl. matem. i matem. fiz., 40:10 (2000), 1475–1490 | MR
[12] Kamenev G. K., Metody approksimatsii vypuklykh tel mnogogrannikami i ikh primenenie dlya postroeniya i analiza obobschennykh mnozhestv dostizhimosti, Dis. ...kand. fiz.-matem. nauk, MFTI, M., 1986, 219 pp.
[13] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR
[14] Rokafellar R., Vypuklyi analiz, Mir, M., 1973
[15] Schneider S., Wieaker J. A., “Approximation of convex bodies by polytopes”, Bull. London Math. Soc., 13(2):41 (1981), 149–156 | DOI | MR | Zbl
[16] Dudley R., “Metric entropy of some classes of sets with differentiable boundaries”, J. Approximat. Theory, 10 (1974), 227–236 ; Corr., 26 (1979), 192–193 | DOI | MR | Zbl | DOI | MR | Zbl
[17] Bronshtein E. M., Ivanov L. D., “O priblizhenii vypuklykh mnozhestv mnogogrannikami”, Sibirskii matem. zh., 26:5 (1975), 1110–1112
[18] Button L., Wilker J.-B., “Cutting exponents for polyhedral approximations to convex bodies”, Geometriac Dedicata, 7:4 (1978), 417–430 | MR
[19] Gruber P. M., “Asymptotic estimates for best and stepwise approximation of convex bodies, I”, Forum Math., 5 (1993), 281–297 | DOI | MR | Zbl
[20] Dzholdybaeva S. M., Kamenev G. K., “Chislennoe issledovanie effektivnosti algoritma approksimatsii vypuklykh tel mnogogrannikami”, Zh. vychisl. matem. i matem. fiz., 32:6 (1992), 857–866 | MR | Zbl