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Applied Mathematical Sciences

Stochastic Approximation Methods for Constrained and Unconstrained Systems

Authors: Kushner, H.J., Clark, D.S.

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About this book

The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric dependence and other qualitative properties of the - gorithms. In this sense, the theory is a statistical version of recursive numerical analysis. The approach taken involves the use of relatively simple compactness methods. Most standard results for Kiefer-Wolfowitz and Robbins-Monro like methods are extended considerably. Constrained and unconstrained problems are treated, as is the rate of convergence problem. While the basic method is rather simple, it can be elaborated to allow a broad and deep coverage of stochastic approximation like problems. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ­ ential equations, has advantages in algorithm conceptualiza­ tion and design. It is often possible to obtain an intuitive understanding of algorithm behavior or qualitative dependence upon parameters, etc., without getting involved in a great deal of deta~l.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-1-4684-9352-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-0-387-90341-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Approximation Methods for Constrained and Unconstrained Systems
Authors
Series Title
Applied Mathematical Sciences
Series Volume
26
Copyright
1978
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-9352-8
DOI
10.1007/978-1-4684-9352-8
Softcover ISBN
978-0-387-90341-5
Series ISSN
0066-5452
Edition Number
1
Number of Pages
X, 263
Topics

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