Geodesic
Adaptive step regulation for a stochastic optimization algorithm
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 6, pp. 1314-1325

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The quasigradient algorithm of stochastic optimization is considered. The conditions to be imposed on the step multiplier, for Cesaro convergence of the algorithms with probability $1$, are studied. Adaptive step adjustment is proposed, and the convergence of the corresponding algorithm is proved. A numerical algorithm containing heuristic elements is described. The results of numerical experiments are quoted. 
@article{ZVMMF_1983_23_6_a3,
     author = {F. Mirzoakhmedov and S. P. Uryasev},
     title = {Adaptive step regulation for a stochastic optimization algorithm},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1314--1325},
     publisher = {mathdoc},
     volume = {23},
     number = {6},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_6_a3/}
}
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F. Mirzoakhmedov; S. P. Uryasev. Adaptive step regulation for a stochastic optimization algorithm. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 6, pp. 1314-1325. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_6_a3/