Geodesic
Piyavskij's method for solving the general global optimization problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 7, pp. 992-1006 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1992_32_7_a1,
     author = {V. I. Norkin},
     title = {Piyavskij's method for solving the general global optimization problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {992--1006},
     year = {1992},
     volume = {32},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_7_a1/}
}
TY  - JOUR
AU  - V. I. Norkin
TI  - Piyavskij's method for solving the general global optimization problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1992
SP  - 992
EP  - 1006
VL  - 32
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_7_a1/
LA  - ru
ID  - ZVMMF_1992_32_7_a1
ER  - 
%0 Journal Article
%A V. I. Norkin
%T Piyavskij's method for solving the general global optimization problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1992
%P 992-1006
%V 32
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_7_a1/
%G ru
%F ZVMMF_1992_32_7_a1
V. I. Norkin. Piyavskij's method for solving the general global optimization problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 7, pp. 992-1006. http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_7_a1/

[1] Cheney E. W., Goldstein A. A., “Newton's method for convex programming and Chebychev approximation”, Numer. Math., 1 (1959), 253–268 | DOI | MR | Zbl

[2] Kelly J. F., “The cutting-plane method for solving convex problems”, SIAM J. Numer. and Appl. Math., 8:4 (1960), 703–712 | DOI | MR

[3] Piyavskii S. A., “Algoritm otyskaniya absolyutnogo minimuma funktsii”, Teoriya optimalnykh reshenii, 2, IK AN USSR, Kiev, 1967, 13–24

[4] Piyavskii S. A., “Odin algoritm otyskaniya absolyutnogo ekstremuma funktsii”, Zh. vychisl. matem. i matem. fiz., 12:4 (1972), 888–896

[5] Demyanov V. F., Rubinov A. M., Priblizhennye metody resheniya ekstremalnykh zadach, Izd-vo LGU, L., 1968

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

[7] Akilov G. P., Rubinov A. M., “Metod posledovatelnykh priblizhenii dlya razyskaniya mnogochlena nailuchshego priblizheniya”, Dokl. AN SSSR, 157:3 (1964), 503–505 | MR | Zbl

[8] Rubinov A. M., “Minimizatsiya normy na kompakte”, Vestn. LGU, 1965, no. 1, 10–15 | MR

[9] Ziyaudinova D. A., Rubinov A. M., “Minimizatsiya sublineinykh funktsionalov na vypuklom kompakte v metrizuemom lokalno-vypuklom prostranstve”, Optimalnoe planirovanie, 7, Nauka, Novosibirsk, 1967, 10–15

[10] Danilin Yu. M., Piyavskii S. A., “Ob odnom algoritme otyskaniya absolyutnogo minimuma”, Teoriya optimalnykh reshenii, 2, IK AN USSR, Kiev, 1967, 25–37 | MR

[11] Danilin Yu. M., “Otsenka effektivnosti odnogo algoritma otyskaniya absolyutnogo minimuma”, Zh. vychisl. matem. i matem. fiz., 11:4 (1971), 1026–1031 | MR | Zbl

[12] Shubert B. O., “A sequential method seeking the global maximum of a function”, SIAM J. Numer. Analys., 2 (1972), 379–388 | DOI | MR

[13] Timonov L. H., “Algoritm poiska globalnogo ekstremuma”, Izv. AN SSSR. Tekhn. kibernetika, 1977, no. 3, 53–60 | Zbl

[14] Bulatov V. P., Metody pogruzheniya v zadachakh optimizatsii, Nauka, Novosibirsk, 1977 | MR | Zbl

[15] Mladineo R. H., “An algorithm for searching the global maximum of a multimodal, multivariate function”, Math. Program., 34 (1986), 188–200 | DOI | MR | Zbl

[16] Mikhalevich V. S., Gupal A. M., Norkin V. I., Metody nevypukloi optimizatsii, Nauka, M., 1987 | MR | Zbl

[17] Antsiferov E. G., Aschepkov L. T., Bulatov V. P., Metody optimizatsii i ikh prilozheniya, v. 1, Matematicheskoe programmirovanie, Nauka, Novosibirsk, 1990 | MR | Zbl

[18] Strongin R. G., Markin D. L., “Minimizatsiya mnogoekstremalnykh funktsii pri nevypuklykh ogranicheniyakh”, Kibernetika, 1986, no. 4, 64–70 | MR

[19] Nemirovskii A. S., Yudin D. B., Slozhnost zadach i effektivnost metodov optimizatsii, Nauka, M., 1980 | MR

[20] Evtushenko Yu. G., “Chislennyi metod poiska globalnogo ekstremuma funktsii (perebor na neravnomernoi setke)”, Zh. vychisl. matem. i matem. fiz., 11:6 (1971), 1390–1403 | Zbl

[21] Perevozchikov A. G., “O slozhnosti vychisleniya globalnogo ekstremuma v odnom klasse mnogoekstremalnykh zadach”, Zh. vychisl. matem. i matem. fiz., 30:3 (1990), 379–387 | MR

[22] Sukharev A. G., Optimalnyi poisk ekstremuma, Izd-vo MGU, M., 1975

[23] Mikhalevich V. S., Trubin V. A., Shor N. Z., Optimizatsionnye zadachi proizvodstvenno-transportnogo planirovaniya, Nauka, M., 1986 | MR

[24] Horst R., Tuy H., Global optimization — deterministic approaches, Springer, Berlin, 1990 | MR

[25] Falk J. E., Hoffman K. L., “A successive underestimation method for concave minimization problems”, Math. Operat. Res., 1:3 (1976), 251–259 | DOI | Zbl

[26] Thien T. V., Tam B. T., Ban V. T., “An outer approximation method for globally minimizing a concave function over a compact convex set”, Acta Meth. Vietnamica, 8 (1983), 21–40 | MR | Zbl

[27] Falk J. E., Hoffman K. L., “Concave minimization via collapsing polytopes”, Operat. Res., 34:6 (1986), 919–929 | DOI | MR | Zbl

[28] Horst R., Thoai N. V., de Vries J., “On finding new vertices and redundant constraints in cutting plane-algorithms for global optimization”, Operat. Res. Letts., 7:2 (1988), 85–90 | DOI | MR | Zbl

[29] Pardalos P. M., Rosen J. B., Constrained global optimization: Algorithms and applications, Lect. Notes Comput. Sci., 268, Springer, Berlin, 1987 | MR | Zbl

[30] Minu M., Matematicheskoe programmirovanie, Nauka, M., 1990 | MR

[31] Shor N. Z., Metody minimizatsii nedifferentsiruemykh funktsii i ikh prilozheniya, Nauk. dumka, Kiev, 1979 | MR | Zbl