Abstract
In this chapter, we will use some simple compactness ideas in order to prove w.p.1 convergence for a variety of unconstrained SA methods. The asymptotic properties of the SA {Xn| sequence will be shown to be the same as the asymptotic properties of the solution to an ordinary differential equation, or generalized ordinary differential equation. We will not aim at the most comprehensive results, but will try to develop the general ideas. The basic idea is simply an extension of the compactness technique as used to construct solutions to ordinary differential equations (Coddington and Levinson [C2], pp. 42–45).
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© 1978 Springer-Verlag New York, Inc.
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Kushner, H.J., Clark, D.S. (1978). Convergence w.p.1 for Unconstrained Systems. In: Stochastic Approximation Methods for Constrained and Unconstrained Systems. Applied Mathematical Sciences, vol 26. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9352-8_2
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DOI: https://doi.org/10.1007/978-1-4684-9352-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90341-5
Online ISBN: 978-1-4684-9352-8
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