Minimizing noisy functionals in Hilbert space: An extension of the Kiefer-Wolfowitz procedure
type: Item
instance of: scholarly article
title: Minimizing noisy functionals in Hilbert space: An extension of the Kiefer-Wolfowitz procedure
zbMATH Open document ID: 0645.62087
DOI: 10.1007/BF01046934
author: Larry Goldstein
published in: Journal of Theoretical Probability
publication date: 1988-01-01T00:00:00Z
review text: The Kiefer-Wolfowitz stochastic approximation procedure can be used for locating of an extremum of a real valued functional g defined on a Hilbert space H. An extension of this procedure for the case of infinite- dimensional Hilbert spaces is presented. The method of random directions is used in such a way that at iteration n attention is restricted to a subspace of finite-dimension \(k_ n\) where \(k_ n\to \infty\). Some necessary restrictions on the functional g must be supposed, the most serious being that in each finite dimensional subspace the functional g should have a ``pseudo-extremum'' and that the sequence of this ``pseudo-extrema'' tends to the ``global'' extremum of g in H. The main convergence theorem is presented and proved. Applications of this procedure to optimal stochastic control are given.
reviewed by: T.Fiala
Mathematics Subject Classification ID: 62L20
zbMATH DE Number: 4052845
zbMATH Keywords: minimizing noisy functionals
zbMATH Keywords: recursive method
zbMATH Keywords: Kiefer-Wolfowitz stochastic approximation procedure
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: method of random directions
zbMATH Keywords: pseudo-extrema
zbMATH Keywords: convergence theorem
zbMATH Keywords: optimal stochastic control
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4052845