Author | Ljung, Lennart. author |
---|---|

Title | Stochastic Approximation and Optimization of Random Systems [electronic resource] / by Lennart Ljung, Georg Pflug, Harro Walk |

Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1992 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-8609-3 |

Descript | VIII, 116 p. online resource |

SUMMARY

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 stochasยญ 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 orยญ 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) ยง1 Almost sure convergence of stochastic approximation procedures 2 ยง2 Recursive methods for linear problems 17 ยง3 Stochastic optimization under stochastic constraints 22 ยง4 A learning model; recursive density estimation 27 ยง5 Invariance principles in stochastic approximation 30 ยง6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug) ยง7 Markovian stochastic optimization and stochastic approximation procedures 53 ยง8 Asymptotic distributions 71 ยง9 Stopping times 79 ยง1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L

CONTENT

I Foundations of stochastic approximation -- ยง1 Almost sure convergence of stochastic approximation procedures -- ยง2 Recursive methods for linear problems -- ยง3 Stochastic optimization under stochastic constraints -- ยง4 A learning model; recursive density estimation -- ยง5 Invariance principles in stochastic approximation -- ยง6 On the theory of large deviations -- References for Part I -- II Applicational aspects of stochastic approximation -- ยง7 Markovian stochastic optimization and stochastic approximation procedures -- ยง8 Asymptotic distributions -- ยง9 Stopping times -- ยง10 Applications of stochastic approximation methods -- References for Part II -- III Applications to adaptation algorithms -- ยง11 Adaptation and tracking -- ยง12 Algorithm development -- ยง13 Asymptotic Properties in the decreasing gain case -- ยง14 Estimation of the tracking ability of the algorithms -- References for Part III

Mathematics
Applied mathematics
Engineering mathematics
Mathematics
Applications of Mathematics