STOCHASTIC APPROXIMATION AND OPTIMIZATION OF RANDOM SYSTEMS IBD

Sinopse

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) º1 Almost sure convergence of stochastic approximation procedures 2 º2 Recursive methods for linear problems 17 º3 Stochastic optimization under stochastic constraints 22 º4 A learning model, recursive density estimation 27 º5 Invariance principles in stochastic approximation 30 º6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug) º7 Markovian stochastic optimization and stochastic approximation procedures 53 º8 Asymptotic distributions 71 º9 Stopping times 79 º1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.