Stochastic Approximation Methods for Constrained and Unconstrained Systems

  • Harold J. Kushner
  • Dean S. Clark

Part of the Applied Mathematical Sciences book series (AMS, volume 26)

Table of contents

  1. Front Matter
    Pages N2-x
  2. Harold J. Kushner, Dean S. Clark
    Pages 1-18
  3. Harold J. Kushner, Dean S. Clark
    Pages 19-99
  4. Harold J. Kushner, Dean S. Clark
    Pages 100-105
  5. Harold J. Kushner, Dean S. Clark
    Pages 106-157
  6. Harold J. Kushner, Dean S. Clark
    Pages 158-208
  7. Harold J. Kushner, Dean S. Clark
    Pages 209-231
  8. Harold J. Kushner, Dean S. Clark
    Pages 232-256
  9. Back Matter
    Pages 257-263

About this book

Introduction

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.

Keywords

Parameter Power Rang Stochastische Approximation probability

Authors and affiliations

  • Harold J. Kushner
    • 1
  • Dean S. Clark
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9352-8
  • Copyright Information Springer-Verlag New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90341-5
  • Online ISBN 978-1-4684-9352-8
  • Series Print ISSN 0066-5452
  • About this book
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