Stochastic Approximation Methods for Constrained and Unconstrained Systems. (= Applied Mathematical Sciences, Vol.26).

Kushner, Harold. J. and Dean. S. Clark:

ISBN 10: 3540903410 / ISBN 13: 9783540903413

Published by Berlin, Springer-Verlag GmbH, 1978

About this Item

x, 261 Seiten Einband etwas berieben, Bibl.Ex., sonst guter und sauberer Zustand 9783540903413 Sprache: Englisch Gewicht in Gramm: 490.

Seller Inventory # 131231

Bibliographic Details

• Title: Stochastic Approximation Methods for Constrained and Unconstrained Systems. (= Applied Mathematical Sciences, Vol.26).
• Publisher: Berlin, Springer-Verlag GmbH
• Publication Date: 1978
• Language: English
• ISBN 10: 3540903410
• ISBN 13: 9783540903413
• Binding: 8° , Softcover/Paperback
• Edition: 1.Auflage,.
• Weight: 490 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

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.