Geodesic
Convergence properties of the gradient method under conditions of variable-level inference
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 997-1007 
S. K. Zavriev. Convergence properties of the gradient method under conditions of variable-level inference. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 997-1007. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a2/
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     title = {Convergence properties of the gradient method under conditions of variable-level inference},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a2/}
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The method of steepest gradient descent is considered on the assumption that the values of the objective function and its gradients are computed inaccurately. The limit set of the trajectories of the method is determined. For some types of noise this set cannot be made smaller for any problem of the class under consideration.

[1] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1989 | MR

[2] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[3] Zavriev S. K., Stokhasticheskie gradientnye metody resheniya minimaksnykh zadach, v. I, Izd-vo MGU, M., 1984 | Zbl

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

[5] Zangvill U., Nelineinoe programmirovanie. Edinyi podkhod, Sov. radio, M., 1973

[6] Kuratovskii K., Topologiya, v. I, Mir, M., 1966 | MR

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