Geodesic
Parallel global optimization of functions of several variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 255-269 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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