A stochastic approximation algorithm with multiplicative step size modification

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A stochastic approximation algorithm with multiplicative step size modification

An algorithm of searching a zero of an unknown function φ : R → R is considered: xt = xt−1 − γt−1yt, t = 1, 2, . . ., where yt = φ(xt−1) + ξt is the value of φ measured at xt−1 and ξt is the measurement error. The step sizes γt > 0 are modified in the course of the algorithm according to the rule: γt = min{u γt−1, ḡ} if yt−1yt > 0, and γt = d γt−1, otherwise, where 0 < d < 1 < u, ḡ > 0. That is...

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© Springer-Verlag, Berlin Heidelberg New York, 1982, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...

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ژورنال

عنوان ژورنال: Mathematical Methods of Statistics

سال: 2009

ISSN: 1066-5307,1934-8045

DOI: 10.3103/s1066530709020057