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

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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. 
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     author = {S. K. Zavriev},
     title = {Convergence properties of the gradient method under conditions of variable-level inference},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {997--1007},
     publisher = {mathdoc},
     volume = {30},
     number = {7},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a2/}
}
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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/