Geodesic
The direct Lyapunov method in investigating the attraction of trajectories of finite-difference inclusions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 1, pp. 22-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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Finite-difference analogues of differential inclusions encountered in the theory of optimization and some other areas are considered. The region of attraction of the trajectories of finite-difference inclusions with respect to an arbitrary Lipschitz Lyapunov function, differentiable with respect to any direction, is investigated. 
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S. K. Zavriev; A. G. Perevozchikov. The direct Lyapunov method in investigating the attraction of trajectories of finite-difference inclusions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 1, pp. 22-32. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a2/

[1] Kosyakin A. A., Shamrikov B. M., Kolebaniya v tsifrovykh avtomaticheskikh sistemakh, Nauka, M., 1983

[2] Tsypkin Ya. Z., Adaptatsiya i obuchenie v avtomaticheskikh sistemakh, Nauka, M., 1968

[3] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl

[4] Ermolev Yu. M., Metody stokhasticheskogo programmirovaniya, Nauka, M., 1976 | MR

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

[6] Nemirovskii A. S., Yudin D. B., Slozhnost zadach i effektivnost metodov optimizatsii, Nauka, M., 1979 | MR

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

[8] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl

[9] Hypminskii E. A., Chislennye metody resheniya determinirovannykh i stokhasticheskikh minimaksnykh zadach, Nauk. dumka, Kiev, 1979 | MR

[10] Rush N., Abets P., Lalua M., Pryamoi metod Lyapunova v teorii ustoichivosti, Mir, M., 1980 | MR

[11] Zavriev S. K., Stokhasticheskie gradientnye metody resheniya minimaksnykh zadach, v. 1, Opyt obschei teorii skhodimosti iteratsionnykh algoritmov optimizatsii, Izd-vo MGU, M., 1984 | Zbl

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

[13] Dorofeev P. A., “O nekotorykh svoistvakh metoda obobschennogo gradienta”, Zh. vychisl. matem. i matem. fiz., 25:2 (1985), 181–189 | MR | Zbl

[14] Aleksandrov P. S., Vvedenie v teoriyu mnozhestv i obschuyu topologiyu, Nauka, M., 1977 | MR

[15] Zangvill U. I., Nelineinoe programmirovanie, Sovetskoe radio, M., 1973

[16] Polyak B. T., “Skhodimost i skorost skhodimosti iterativnykh stokhasticheskikh algoritmov. 1: Obschii sluchai”, Avtomatika i telemekhan., 1976, no. 12, 83–94 | MR | Zbl