Show simple item record Plakhov, A. Y. Cruz, P. 2008-12-08T10:28:41Z 2008-12-08T10:28:41Z 2004-03
dc.identifier.citation Plakhov , A Y & Cruz , P 2004 , ' A stochastic approximation algorithm with step size adaptation ' Journal of Mathematical Sciences , vol 120 , no. 1 , pp. 964-973 . DOI: 10.1023/B:JOTH.0000013559.37579.b2 en
dc.identifier.issn 1072-3374
dc.identifier.other PURE: 89013
dc.identifier.other PURE UUID: 2efd673e-b69c-44c8-b0b1-ed301bc4e043
dc.identifier.other dspace: 2160/1431
dc.identifier.other DSpace_20121128.csv: row: 1114
dc.description Plakhov, A.Y.; Cruz, P., (2004) 'A stochastic approximation algorithm with step size adaptation', Journal of Mathematical Science 120(1) pp.964-973 RAE2008 en
dc.description.abstract We consider the following stochastic approximation algorithm of searching for the zero point x∗ of a function ϕ: xt+1 = xt − γtyt, yt = ϕ(xt) + ξt, where yt are observations of ϕ and ξt is the random noise. The step sizes γt of the algorithm are random, the increment γt+1 − γt depending on γt and on yt yt−1 in a rather general form. Generally, it is meant that γt increases as ytyt−1 > 0, and decreases otherwise. It is proved that the algorithm converges to x∗ almost surely. This result generalizes similar results of Kesten (1958) and Plakhov and Almeida (1998), where γt+1 − γt is assumed to depend only on γt and sgn(ytyt−1) and not on the magnitude of ytyt−1. en
dc.format.extent 10 en
dc.language.iso eng
dc.relation.ispartof Journal of Mathematical Sciences en
dc.rights en
dc.title A stochastic approximation algorithm with step size adaptation en
dc.type /dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article en
dc.contributor.institution Department of Physics en
dc.contributor.institution Mathematics and Physics en
dc.description.status Peer reviewed en

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