Geodesic
Parallel global optimization of functions of several variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 255-269 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

On the basis of the method of nonuniform coverings, a parallel method for the global optimization of Lipschitzian functions is developed. This method is implemented in C-MPI for the global minimization of functions whose gradient satisfies the Lipschitz condition. The performance of the algorithm is demonstrated using the calculation of the structure of a protein molecule as an example. 
@article{ZVMMF_2009_49_2_a4,
     author = {Yu. G. Evtushenko and V. U. Malkova and A.-I. A. Stanevichyus},
     title = {Parallel global optimization of functions of several variables},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {255--269},
     year = {2009},
     volume = {49},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a4/}
}
TY  - JOUR
AU  - Yu. G. Evtushenko
AU  - V. U. Malkova
AU  - A.-I. A. Stanevichyus
TI  - Parallel global optimization of functions of several variables
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 255
EP  - 269
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a4/
LA  - ru
ID  - ZVMMF_2009_49_2_a4
ER  - 
%0 Journal Article
%A Yu. G. Evtushenko
%A V. U. Malkova
%A A.-I. A. Stanevichyus
%T Parallel global optimization of functions of several variables
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 255-269
%V 49
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a4/
%G ru
%F ZVMMF_2009_49_2_a4
Yu. G. Evtushenko; V. U. Malkova; A.-I. A. Stanevichyus. Parallel global optimization of functions of several variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 255-269. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a4/

[1] Strongin R. C., Sergeyev Y. D., Global optimization with non-convex constraints, Sequential and parallel algorithms, Kluwer Acad. Publ., Dordrecht etc., 2000 | MR | Zbl

[2] Voevodin V. V., Voevodin Vl. V., Parallelnye vychisleniya, BKhV-Peterburg, SPb., 2002

[3] 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

[4] Evtushenko Yu. G., Ratkin V. A., “Metod polovinnykh delenii dlya globalnoi optimizatsii funktsii mnogikh peremennykh”, Tekhn. kibernetika, 1987, no. 1, 119–127 | MR | Zbl

[5] Belyankov A. Ya., “Povyshenie vychislitelnoi effektivnosti metodov neravnomernykh pokrytii v globalnoi optimizatsii”, Metody matem. programmirovaniya i programmnoe obespechenie, Tezisy dokl., UrO AN SSSR, Sverdlovsk, 1989, 21–22 | MR

[6] Evtushenko Yu. G., Malkova V. U., Stanevichyus A. A., “Rasparallelivanie protsessa poiska globalnogo ekstremuma”, Avtomatika i telemekhan., 2007, no. 5, 46–58 | MR | Zbl

[7] Nesterov Yu., Polyak B., “Cubic regularization of Newton method and its global performance”, Math. Program., 108:1 (2006), 177–205 | DOI | MR | Zbl

[8] Strekalovskii A. C., Elementy nevypukloi optimizatsii, Nauka, Novosibirsk, 2003

[9] Belyankov A. Ya., “Predvaritelnoe droblenie parallelepipeda v metodakh neravnomernykh pokrytii v globalnoi optimizatsii”, II Vseros. nauchn. konf. s molodezhnoi nauchn. shkoloi “Matem. modelirovanie razvivayuscheisya ekonomiki”. EKOMOD-2007, Izd-vo VyatGU, Kirov, 2007, 59–62

[10] Posypkin M. A., Sigal I. Kh., “Issledovanie algoritmov parallelnykh vychislenii v zadachakh diskretnoi optimizatsii rantsevogo tipa”, Zh. vychisl. matem. i matem. fiz., 45:10 (2005), 1801–1809 | MR

[11] Mezhvedomstvennyi superkompyuternyi tsentr Rossiiskoi akademii nauk, Web-sait: http://www.jscc.ru

[12] Cambridge Cluster Database, Web-sait: http://www-wales.ch.cam.ac.uk/~jon/structures/Morse.html

[13] Evtushenko Yu. G., Potapov M. A., “Metody resheniya mnogokriterialnykh zadach”, Dokl. AN SSSR, 291:1 (1986), 25–29 | MR | Zbl

[14] Evtushenko Yu. G., “Chislennyi metod otyskaniya nailuchshikh garantirovannykh otsenok”, Zh. vychisl. matem. i matem. fiz., 12:1 (1972), 89–104