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.
