Stochastic Approximation Methods for Constrained and Unconstrained Systems

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 t

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Lawrence Sirovich

Courant Institute of Mathematical Sciences New York University New York, N.Y. 10012

Division of Applied Mathematics Brown University Providence, R.I. 02912

Joseph P. LaSalle

Gerald B. Whitham

Division of Applied Mathematics Brown University Providence, R.L 02912

Applied Mathematics Firestone Laboratory California Institute of Technology Pasadena, CA.91125

EDITORIAL STATEMENT The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of mathematicalcomputer modelling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The purpose of this series is to provide such books, suitable for the user of mathematics, the mathematician interested in applications, and the student scientist. In particular, this series will provide an outlet for material less formally presented and more anticipatory of needs than finished texts or monographs, yet of immediate interest because of the novelty of its treatment of an application or of mathematics being applied or Iying close to applications. The aim of the series is, through rapid publication in an attractive but inexpensive format, to make material of current interest widely accessible. This implies the absence of excessive generality and abstraction, and unrealistic idealization, but with quality of exposition as a goal. Many of the books will originate out of and will stimulate the development of new undergraduate and graduate courses in the applications of mathematics. Some of the books will present introductions to new areas of research, new applications and act as signposts for new directions in the mathematical sciences. This series will often serve as an intermediate stage of the publication of material which, through exposure here, will be further developed and refined. These will appear in conventional format and in hard cover.

MANUSCRIPTS The Editors welcome all inquiries regarding the submission of manuscripts for the series. Final preparation of all manuscripts will take place in the editorial offices of the series in the Division of Applied Mathematics, Brown University, Providence, Rhode Island. SPRINGER-VERLAG NEW YORK INe., 175 Fifth Avenue, New York, N. Y. 10010

Applied Mathematical Sciences I Volume 26

Harold J. Kush ner Dean S. Clark

Stochastic Approximation Methods for Constrained and Unconstrained Systems

Springer-Verlag

New York

Heidelberg

Berlin

Harold J. Kushner Division of Applied Mathematics Brown University Providence, Rhode Island USA

Dean S. Clark Division of Applied Mathematics Brown University Providence, Rhode Island USA

AMS Classifications: 41A65, 34F05, 60H10, 60H15, 62N15, 93E10

Ubrary of Congress Cataloging in Publication Data

Kushner, Harold Joseph, 1933Stochastic approximation methods for constrained and unconstrained systems. (Applied mathematical sciences; 26) Bibliography: p. Includes index. 1. Stochastic appro

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