On the convergence of the conditional gradient method in distributed optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1616-1629 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem is stated on sufficient conditions for the convergence of the conditional gradient method as applied to the optimization of a nonlinear controlled functional–operator equation in a Banach ideal space. The theory is illustrated by application to the controlled Goursat–Darboux problem.
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A. V. Chernov. On the convergence of the conditional gradient method in distributed optimization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1616-1629. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a4/

[1] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl

[2] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[3] Sumin V. I., “Ob obosnovanii gradientnykh metodov dlya raspredelennykh zadach optimalnogo upravleniya”, Zh. vychisl. matem. i matem. fiz., 30:1 (1990), 3–21 | MR | Zbl

[4] Sumin V. I., Funktsionalnye volterrovy uravneniya v teorii optimalnogo upravleniya raspredelennymi sistemami, ch. I, NNGU, N. Novgorod, 1992

[5] Sumin V. I., Chernov A. V., “O dostatochnykh usloviyakh ustoichivosti suschestvovaniya globalnykh reshenii volterrovykh operatornykh uravnenii”, Vestn. Nizhegorodskogo un-ta. Ser. Matem. modelirovanie i optimalnoe upravlenie, 2003, no. 1(26), 39–49

[6] Chernov A. V., “O totalnom sokhranenii globalnoi razreshimosti funktsionalno-operatornykh uravnenii”, Vestn. Nizhegorodskogo un-ta. Ser. Matematika, 2009, no. 3, 130–137 | MR

[7] Chernov A. V., “O potochechnoi otsenke raznosti reshenii upravlyaemogo funktsionalno-operatornogo uravneniya v lebegovykh prostranstvakh”, Matem. zametki, 88:2 (2010), 288–302 | Zbl

[8] Chernov A. V., “Ob odnom mazhorantnom priznake totalnogo sokhraneniya globalnoi razreshimosti upravlyaemogo funktsionalno-operatornogo uravneniya”, Izv. vuzov. Matematika, 2011, no. 3, 95–107 | Zbl

[9] Sumin V. I., “Funktsionalno-operatornye volterrovy uravneniya v teorii optimalnogo upravleniya raspredelennymi sistemami”, Dokl AN SSSR, 305:5 (1989), 1056–1059 | MR | Zbl

[10] Sumin V. I., “O funktsionalnykh volterrovykh uravneniyakh”, Izv. vuzov. Matematika, 1995, no. 9, 67–77 | MR | Zbl

[11] Sumin V. I., “Upravlyaemye funktsionalnye volterrovy uravneniya v lebegovykh prostranstvakh”, Vestn. Nizhegorodskogo un-ta. Ser. Matem. modelirovanie i optimalnoe upravlenie, 1998, no. 2(19), 138–151

[12] Sumin V. I., Chernov A. V., “Operatory v prostranstvakh izmerimykh funktsii: volterrovost i kvazinilpotentnost”, Differents. ur-niya, 34:10 (1998), 1402–1411 | MR | Zbl

[13] Sumin V. I., Chernov A. V., “O nekotorykh priznakakh kvazinilpotentnosti funktsionalnykh operatorov”, Izv. vuzov. Matematika, 2000, no. 2, 77–80 | MR | Zbl

[14] Mordukhovich B. Sh., Metody approksimatsii v zadachakh optimizatsii i upravleniya, Nauka, M., 1988 | MR | Zbl

[15] Danford N., Shvarts Dzh., Lineinye operatory, v. 1, Obschaya teoriya, Izd-vo inostr. lit., M., 1962