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Stochastic Approximation and Optimization of Random Systems (Paperback, 1992 ed.)
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Stochastic Approximation and Optimization of Random Systems (Paperback, 1992 ed.)
Series: Oberwolfach Seminars, 17
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The DMV seminar "Stochastische Approximation und Optimierung
zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The
goal was to give an approach to theory and application of stochas
tic approximation in view of optimization problems, especially in
engineering systems. These notes are based on the seminar lectures.
They consist of three parts: I. Foundations of stochastic
approximation (H. Walk); n. Applicational aspects of stochastic
approximation (G. PHug); In. Applications to adaptation: ugorithms
(L. Ljung). The prerequisites for reading this book are basic
knowledge in probability, mathematical statistics, optimization. We
would like to thank Prof. M. Barner and Prof. G. Fischer for the or
ganization of the seminar. We also thank the participants for their
cooperation and our assistants and secretaries for typing the
manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of
contents I Foundations of stochastic approximation (H. Walk) 1
Almost sure convergence of stochastic approximation procedures 2 2
Recursive methods for linear problems 17 3 Stochastic optimization
under stochastic constraints 22 4 A learning model; recursive
density estimation 27 5 Invariance principles in stochastic
approximation 30 6 On the theory of large deviations 43 References
for Part I 45 11 Applicational aspects of stochastic approximation
(G. PHug) 7 Markovian stochastic optimization and stochastic
approximation procedures 53 8 Asymptotic distributions 71 9
Stopping times 79 1O Applications of stochastic approximation
methods 80 References for Part II 90 III Applications to adaptation
algorithms (L."
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