Geodesic
Homogeneous algorithms for multiextremal optimization
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 10, pp. 1727-1740 Cet article a éte moissonné depuis la source Math-Net.Ru

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The class of homogeneous algorithms for multiextremal optimization is defined, and a number of theorems are proved, including a sufficient condition for the convergence of homogeneous algorithms to a global minimizer. An approach to the synthesis of homogeneous algorithms based on model multi-peak functions is proposed. The existing algorithms are reviewed, and a new efficient multidimensional algorithm based on the Delaunay triangulation is constructed. Some numerical results are presented. 
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S. M. Elsakov; V. I. Shiryaev. Homogeneous algorithms for multiextremal optimization. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 10, pp. 1727-1740. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_10_a1/

[1] Antonov M. O., Elsakov S. M., Shiryaev V. I., “Nakhozhdenie optimalnogo raspolozheniya radiomayakov v raznostno-dalnomernoi sisteme posadki letatelnogo apparata”, Aviakosmich. priborostroenie, 2005, no. 11, 41–45

[2] Gergel V. P., Gorodetskii S. Yu., Grishagin V. P., Strongin R. G., Sovremennye metody prinyatiya optimalnykh reshenii, Izd-vo NNGU, N. Novgorod, 2002

[3] Horst R., Pardalos P., Thoai N., Introduction to global optimization, 2nd ed., Kluwer Acad. Publs, Dordrecht, 2000 | MR

[4] Zhiglyavskii A. A., Matematicheskaya teoriya globalnogo sluchainogo poiska, Izd-vo LGU, L., 1985 | MR

[5] Zhiglyavskii A. A., Zhilinskas A. G., Metody poiska globalnogo ekstremuma, Nauka, M., 1991 | MR

[6] Zhilinskas A. G., Globalnaya optimizatsiya: Aksiomatika statisticheskikh modelei, algoritmy, primeneniya, Mokslas, Vilnyus, 1986 | MR

[7] Kvasov D. E., Sergeev Ya. D., “Mnogomernyi algoritm globalnoi optimizatsii na osnove adaptivnykh diagonalnykh krivykh”, Zh. vychisl. matem. i matem. fiz., 43:1 (2003), 42–59 | MR

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

[9] Strongin R. G., Chislennye metody v mnogoekstremalnykh zadachakh, Nauka, M., 1978 | MR | Zbl

[10] Rozanov Yu. A., Sluchainye polya i stokhasticheskie uravneniya s chastnymi proizvodnymi, Nauka, M., 1995 | MR | Zbl

[11] Skvortsov A. V., Triangulyatsiya Delone i ee primenenie, Izd-vo Tomskogo un-ta, Tomsk, 2002

[12] Preparata F., Sheimos M., Vychislitelnaya geometriya: Vvedenie, Mir, M., 1989 | MR | Zbl

[13] Rajan V. T., “Optimality of Delaunay triangulation in $\mathbb{R}^N$”, Proc. 7th ACM Symp. Comp. Geometry, 1991, 357–363

[14] Gorodetskii S. Yu., “Mnogoekstremalnaya optimizatsiya na osnove triangulyatsii oblasti”, Matem. modelirovanie i optimalnoe upravlenie, Vestn. Nizhegorodskogo gos. un-ta, 2 (21), Izd-vo NNGU, N. Novgorod, 1999, 249–269

[15] Gorodetskii S. Yu., SM-metody v zadachakh mnogoekstremalnoi optimizatsii s ogranicheniyami dlya klassa funktsii s lipshitsevymi proizvodnymi po napravleniyam, Dep. V VINITI 11.01.07 No 18-V2007, fak. VMK NNGU, N. Novgorod, 2007, 22 pp.

[16] Polyanin A. D., Zaitsev V. F., Spravochnik po nelineinym uravneniyam matematicheskoi fiziki: Tochnye resheniya, Fizmatlit, M., 2002 | MR

[17] Zhilinskas A. G., “Odnoshagovyi baiesovskii metod poiska ekstremuma funktsii odnoi peremennoi”, Kibernetika, 1 (1975), 139–144 | Zbl

[18] Kushner H., “A New method of locating the maximum point of an arbitrary multipeak curve in the presence of noise”, Transactions ASME. Ser. D. J. Basic Engng., 86:1 (1964), 97–106 | MR

[19] Grishagin V. A., “Ob usloviyakh skhodimosti dlya odnogo klassa algoritmov globalnogo poiska”, Chisl. metody nelineinogo programmirovaniya, Tezisy dokl. III Vses. seminara, KhGU, Kharkov, 1979, 82–84

[20] Gorodetskii S. Yu., “Skhodimost i asimptoticheskie otsenki povedeniya dlya odnogo klassa metodov poiska”, Dinamika sistem. Dinamika i upravlenie, GGU, Gorkii, 1984 | MR

[21] Sergeyev Ya. D., “On convergence of “Divide the best” global optimization algorithms”, Optimization, 44 (1998), 303–325 | DOI | MR | Zbl

[22] Pinter J. D., “Extended univariate algoritms for $\mathrm{N}$-dimensional global optimization”, Computing, 36:1–2 (1986), 91–103 | DOI | MR | Zbl