Geodesic
The method of generalized stochastic gradient for solving minimax problems with constrained variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 491-500 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Minimax problems with constrained variables are considered. It is shown that under specified assumptions the internal maximum function is differentiable in the sense of Clarke and regular. The method of generalized stochastic gradient is proposed to minimize the function in the presence of constraints. It is shown how the parameters of the method can be made consistent with the convergence of a “diagonal” procedure of the Arrow-Hurewicz type in the case where the internal maximization problem is concave. . 
@article{ZVMMF_1990_30_4_a1,
     author = {S. K. Zavriev and A. G. Perevozchikov},
     title = {The method of generalized stochastic gradient for solving minimax problems with constrained variables},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {491--500},
     year = {1990},
     volume = {30},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a1/}
}
TY  - JOUR
AU  - S. K. Zavriev
AU  - A. G. Perevozchikov
TI  - The method of generalized stochastic gradient for solving minimax problems with constrained variables
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 491
EP  - 500
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a1/
LA  - ru
ID  - ZVMMF_1990_30_4_a1
ER  - 
%0 Journal Article
%A S. K. Zavriev
%A A. G. Perevozchikov
%T The method of generalized stochastic gradient for solving minimax problems with constrained variables
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 491-500
%V 30
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a1/
%G ru
%F ZVMMF_1990_30_4_a1
S. K. Zavriev; A. G. Perevozchikov. The method of generalized stochastic gradient for solving minimax problems with constrained variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 491-500. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a1/

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

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

[3] Minchenko L. I., “Differentsialnye svoistva funktsii maksimuma pri svyazannykh ogranicheniyakh”, Zh. vychisl. matem. i matem. fiz., 24:2 (1984), 210–217 | MR | Zbl

[4] Rekleitis G., Reivindran A.,, Regsdel K., Optimizatsiya v tekhnike, Mir, M., 1986

[5] Gill F., Myurrei U., Rait M., Prakticheskaya optimizatsiya, Mir, M., 1985 | MR

[6] Zavriev S. K., Perevozchikov A. G., “Pryamoi metod Lyapunova v issledovanii prityazheniya traektorii konechno-raznostnykh vklyuchenii”, Zh. vychisl. matem. i matem. fiz., 30:1 (1990), 22–32 | MR | Zbl

[7] Pshenichnyi B. N., Neobkhodimye usloviya ekstremuma, Nauka, M., 1969 | MR

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

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

[10] Gaivoronskii A. A., Issledovanie nestatsionarnykh zadach stokhasticheskogo programmirovaniya, Avtoref. dis. ...kand. fiz.-matem. nauk, IK AN USSR, Kiev, 1979