Stochastic Approximation And Optimization Of Random Systems
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Stochastic Approximation And Optimization Of Random Systems
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Author : Lennart Ljung
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-03-31
Stochastic Approximation And Optimization Of Random Systems written by Lennart Ljung and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-31 with Mathematics categories.
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.
Stochastic Approximation And Recursive Algorithms And Applications
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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-04
Stochastic Approximation And Recursive Algorithms And Applications written by Harold Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-04 with Mathematics categories.
The basic stochastic approximation algorithms introduced by Robbins and MonroandbyKieferandWolfowitzintheearly1950shavebeenthesubject of an enormous literature, both theoretical and applied. This is due to the large number of applications and the interesting theoretical issues in the analysis of “dynamically de?ned” stochastic processes. The basic paradigm is a stochastic di?erence equation such as ? = ? + Y , where ? takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the “step n size” > 0 is small and might go to zero as n??. In its simplest form, n ? is a parameter of a system, and the random vector Y is a function of n “noise-corrupted” observations taken on the system when the parameter is set to ? . One recursively adjusts the parameter so that some goal is met n asymptotically. Thisbookisconcernedwiththequalitativeandasymptotic properties of such recursive algorithms in the diverse forms in which they arise in applications. There are analogous continuous time algorithms, but the conditions and proofs are generally very close to those for the discrete time case. The original work was motivated by the problem of ?nding a root of a continuous function g ̄(?), where the function is not known but the - perimenter is able to take “noisy” measurements at any desired value of ?. Recursive methods for root ?nding are common in classical numerical analysis, and it is reasonable to expect that appropriate stochastic analogs would also perform well.
Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory
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Author : Harold Joseph Kushner
language : en
Publisher: MIT Press
Release Date : 1984
Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory written by Harold Joseph Kushner and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Computers categories.
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Stochastic Approximation And Its Applications
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Author : Han-Fu Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-30
Stochastic Approximation And Its Applications written by Han-Fu Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-30 with Mathematics categories.
Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Stochastic Approximation
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Author : Vivek S. Borkar
language : en
Publisher: Springer
Release Date : 2009-01-01
Stochastic Approximation written by Vivek S. Borkar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
Lectures On Stochastic Programming
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Author : Alexander Shapiro
language : en
Publisher: SIAM
Release Date : 2009-10-08
Lectures On Stochastic Programming written by Alexander Shapiro and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Mathematics categories.
A comprehensive treatment of optimization problems involving uncertain parameters for which stochastic models are available.
Stochastic Recursive Algorithms For Optimization
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Author : S. Bhatnagar
language : en
Publisher: Springer
Release Date : 2012-08-12
Stochastic Recursive Algorithms For Optimization written by S. Bhatnagar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-12 with Technology & Engineering categories.
Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from similarly diverse backgrounds: workers in relevant areas of computer science, control engineering, management science, applied mathematics, industrial engineering and operations research will find the content of value.
Stochastic Approximation
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Author : M. T. Wasan
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03
Stochastic Approximation written by M. T. Wasan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Mathematics categories.
A rigorous mathematical treatment of the technique for studying the properties of an experimental situation.
Stochastic Optimization Methods
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Author : Kurt Marti
language : en
Publisher: Springer
Release Date : 2015-02-21
Stochastic Optimization Methods written by Kurt Marti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-21 with Business & Economics categories.
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
Random Iterative Models
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Author : Marie Duflo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Random Iterative Models written by Marie Duflo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Be they random or non-random, iterative methods have progressively gained sway with the development of computer science and automatic control theory. Thus, being easy to conceive and simulate, stochastic processes defined by an iterative formula (linear or functional) have been the subject of many studies. The iterative structure often leads to simpler and more explicit arguments than certain classical theories of processes. On the other hand, when it comes to choosing step-by-step decision algorithms (sequential statistics, control, learning, ... ) recursive decision methods are indispensable. They lend themselves naturally to problems of the identification and control of iterative stochastic processes. In recent years, know-how in this area has advanced greatly; this is reflected in the corresponding theoretical problems, many of which remain open. At Whom Is This Book Aimed? I thought it useful to present the basic ideas and tools relating to random iterative models in a form accessible to a mathematician familiar with the classical concepts of probability and statistics but lacking experience in automatic control theory. Thus, the first aim of this book is to show young research workers that work in this area is varied and interesting and to facilitate their initiation period. The second aim is to present more seasoned probabilists with a number of recent original techniques and arguments relating to iterative methods in a fairly classical environment.