A class of adaptive algorithms for approximating convex bodies by polyhedra
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 1, pp. 136-152 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1992_32_1_a10,
     author = {G. K. Kamenev},
     title = {A class of adaptive algorithms for approximating convex bodies by polyhedra},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {136--152},
     year = {1992},
     volume = {32},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_1_a10/}
}
TY  - JOUR
AU  - G. K. Kamenev
TI  - A class of adaptive algorithms for approximating convex bodies by polyhedra
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1992
SP  - 136
EP  - 152
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_1_a10/
LA  - ru
ID  - ZVMMF_1992_32_1_a10
ER  - 
%0 Journal Article
%A G. K. Kamenev
%T A class of adaptive algorithms for approximating convex bodies by polyhedra
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1992
%P 136-152
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_1_a10/
%G ru
%F ZVMMF_1992_32_1_a10
G. K. Kamenev. A class of adaptive algorithms for approximating convex bodies by polyhedra. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 1, pp. 136-152. http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_1_a10/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961

[2] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR | Zbl

[3] Chernousko F. L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem. Metod ellipsoidov, Nauka, M., 1988 | MR

[4] Kirillova L. S., “Obschaya zadacha terminalnogo upravleniya v lineinykh sistemakh”, Avtomatika i telemekhan., 26:12 (1965), 2120–2130 | MR | Zbl

[5] Formalskii A. M., “Postroenie oblasti upravlyaemosti sistem s ogranichennymi resursami upravleniya”, Avtomatika i telemekhan., 1968, no. 3, 21–29 | MR

[6] Pecsvaradi T., Narendra K. S., “Reachable sets for linear dynamic systems”, Information and Control, 19:4 (1971), 230–248 | DOI | MR

[7] Lotov A. V., “Chislennyi metod postroeniya mnozhestv dostizhimosti dlya lineinykh upravlyaemykh sistem s fazovymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 15:1 (1975), 67–68 | MR

[8] Sonnevend G., “On optimization of algorithms for function minimization”, Zh. vychisl. matem. i matem. fiz., 17 (1977), 591–609 | MR | Zbl

[9] Mukhamediev B. M., “Priblizhennyi metod resheniya zadachi vognutogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 22:3 (1982), 727–732 | MR | Zbl

[10] Vasilev N. S., “K otyskaniyu globalnogo minimuma kvazivognutoi funktsii”, Zh. vychisl. matem. i matem. fiz., 23:2 (1983), 307–313 | MR

[11] Lotov A. V., “O ponyatii obobschennykh mnozhestv dostizhimosti i ikh postroenii dlya lineinykh upravlyaemykh sistem”, Dokl. AN SSSR, 250:5 (1980), 1081–1083 | MR | Zbl

[12] Lotov A. V., “Analiz potentsialnykh vozmozhnostei ekonomicheskikh sistem”, Ekonomika i matem. metody, 17:2 (1981), 377–381 | MR | Zbl

[13] Lotov A. V., “Agregirovanie kak approksimatsiya obobschennykh mnozhestv dostizhimosti”, Dokl. AN SSSR, 265:6 (1982), 1134–1137

[14] Lotov A. V., Vvedenie v ekonomiko-matematicheskoe modelirovanie, Nauka, M., 1984 | MR | Zbl

[15] Bushenkov V. A., Kamenev G. K., Lotov A. V., Chernykh O. L., “Ispolzovanie geometricheskogo metoda dlya analiza ekologo-ekonomicheskikh sistem”, Matem. modelirovanie. Protsessy v slozhnykh ekonomich. i ekologich. sistemakh, Nauka, M., 1986, 240–252

[16] Gruber P. M., “Approximation of convex bodies”, Convexity and its Appl., Birkhäuser, Basel etc., 1983, 131–162 | MR

[17] Yudin D. B., Nemirovskii A. S., “Otsenka informatsionnoi slozhnosti zadach matematicheskogo programmirovaniya”, Ekonomika i matem. metody, 12:1 (1976), 128–142 | MR | Zbl

[18] Minkowski H., “Volumen und Oberfläche”, Math. Ann., 57 (1903), 447–495 | DOI | MR | Zbl

[19] Bushenkov V. A., “Metod sinteza sechenii dlya approksimatsii ortogonalnykh proektsii mnogogrannykh mnozhestv”, Metody matem. programmirovaniya i programmnoe obespechenie, Tezisy dokl. VI nauchn. konf., UrO AN SSSR, Sverdlovsk, 1989, 31

[20] Schneider R., “Zur optimalen Approximation konvexer Hyperflächen durch Polyeder”, Math. Ann., 256:3 (1983), 289–301 | DOI | MR

[21] Schneider R., “Polyhedral approximation of smooth convex bodies”, J. Math. Analys. and Applic., 128:2 (1987), 470–474 | DOI | MR | Zbl

[22] Gruber P. M., “Volume approximation of convex bodies by inscribed polytopes”, Math. Ann., 281:2 (1988), 229–245 | DOI | MR | Zbl

[23] McClure D. E., Vitale R. A., “Polygonal approximation of plane convex bodies”, J. Math. Analys. and Applic., 51:2 (1975), 326–358 | DOI | MR | Zbl

[24] Sonnevend Gy., “Asymptotically optimal, sequential methods for the approximation of convex, compact sets in $\mathbb{R}^d$ in the Hausdorff metrics”, Colloquia Math. Soc. Janos Bolyai, 35(2), 1980, 1075–1089 | MR

[25] Samsonov S. P., “Vosstanovlenie vypuklogo mnozhestva po ego opornoi funktsii s zadannoi tochnostyu”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1983, no. 1, 68–71 | MR | Zbl

[26] Vasilev N. S., “O neuluchshaemykh otsenkakh approksimatsii silno vypuklykh tel”, Vopr. kibernetiki, 136 (1988), 49–56 | MR

[27] Appino P. A., A solution technique for approximating the non-inferior set of three objective linear programs, Ph. D. Diss., Johns Hopkins Univ., Baltimore, Maryland, 1984

[28] Bushenkov V. A., “Chislennyi algoritm postroeniya proektsii mnogogrannykh mnozhestv”, Aerofiz. i prikl. matem., MFTI, M., 1981, 108–110

[29] Bushenkov V. A., Lotov A. V., Metody postroeniya i ispolzovaniya obobschennykh mnozhestv dostizhimosti, VTs AN SSSR, M., 1982

[30] Bushenkov V. A., “Iteratsionnyi metod postroeniya ortogonalnykh proektsii vypuklykh mnogogrannykh mnozhestv”, Zh. vychisl. matem. i matem. fiz., 25:9 (1985), 1285–1292 | MR | Zbl

[31] Kamenev G. K., Issledovanie iteratsionnykh metodov approksimatsii vypuklykh mnozhestv mnogogrannikami, VTs AN SSSR, M., 1986

[32] 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

[33] Sonnevend G., “An optimal sequential algorithm for uniform approximation of convex functions on $[0, 1]^2$”, Appl. Math. and Optimizat., 1983, no. 10, 127–142 | DOI | MR | Zbl

[34] Kamenev G. K., “Ob odnom klasse adaptivnykh skhem approksimatsii vypuklykh tel mnogogrannikami”, Matem. modelirovanie i diskretnaya optimizatsiya, VTs AN SSSR, M., 1988, 3–9 | MR

[35] Cohon J. L., Multiobjective programming and planning, Acad. Press, N. Y., 1978 | MR | Zbl

[36] Schneider R., Wieacker J. A., “Approximation of convex bodies by polytopes”, Bull. London Math. Soc., 13 (2):41 (1981), 149–156 | DOI | MR | Zbl

[37] Gruber P. M., Kendrov P., “Approximation of convex bodies by polytopes”, Rendiconti Circolo mat. Palermo. Ser. 2, 31:2 (1982), 195–225 | DOI | MR | Zbl

[38] Button L., Wilker J.-B., “Cutting exponents for polyhedral approximations to convex bodies”, Geometriae Bedicata, 7:4 (1978), 417–430 | MR

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

[40] Blyashke V., Krug i shar, Nauka, M., 1967 | MR

[41] Koutroufiotis D., “On Blaschke's rolling theorems”, Arch. Math., 23 (1972), 655–660 | DOI | MR | Zbl