Stochastic Approximation And Optimization Of Random Systems

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Stochastic Approximation and Optimization of Random Systems

Author : L. Ljung
Publisher : Birkhäuser
ISBN 13 : 3034886098
Total Pages : 120 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Stochastic Approximation and Optimization of Random Systems by : L. Ljung

Download or read book Stochastic Approximation and Optimization of Random Systems written by L. Ljung and published by Birkhäuser. This book was released on 2012-12-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Optimization of Random Systems

Author : Lennart Ljung
Publisher : Birkhäuser
ISBN 13 : 9783764327330
Total Pages : 0 pages
Book Rating : 4.3/5 (273 download)

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Book Synopsis Stochastic Approximation and Optimization of Random Systems by : Lennart Ljung

Download or read book Stochastic Approximation and Optimization of Random Systems written by Lennart Ljung and published by Birkhäuser. This book was released on 1992-03-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Harold Kushner
Publisher : Springer Science & Business Media
ISBN 13 : 038721769X
Total Pages : 478 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Stochastic Approximation and Recursive Algorithms and Applications by : Harold Kushner

Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory

Author : Harold Joseph Kushner
Publisher : MIT Press
ISBN 13 : 9780262110907
Total Pages : 296 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory by : Harold Joseph Kushner

Download or read book Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory written by Harold Joseph Kushner and published by MIT Press. This book was released on 1984 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Methods for Constrained and Unconstrained Systems

Author : H.J. Kushner
Publisher : Springer Science & Business Media
ISBN 13 : 1468493523
Total Pages : 273 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Stochastic Approximation Methods for Constrained and Unconstrained Systems by : H.J. Kushner

Download or read book Stochastic Approximation Methods for Constrained and Unconstrained Systems written by H.J. Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric dependence and other qualitative properties of the - gorithms. In this sense, the theory is a statistical version of recursive numerical analysis. The approach taken involves the use of relatively simple compactness methods. Most standard results for Kiefer-Wolfowitz and Robbins-Monro like methods are extended considerably. Constrained and unconstrained problems are treated, as is the rate of convergence problem. While the basic method is rather simple, it can be elaborated to allow a broad and deep coverage of stochastic approximation like problems. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design. It is often possible to obtain an intuitive understanding of algorithm behavior or qualitative dependence upon parameters, etc., without getting involved in a great deal of deta~l.

Stochastic Approximation and Its Applications

Author : Han-Fu Chen
Publisher : Springer Science & Business Media
ISBN 13 : 0306481669
Total Pages : 360 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Stochastic Approximation and Its Applications by : Han-Fu Chen

Download or read book Stochastic Approximation and Its Applications written by Han-Fu Chen and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Stochastic Search and Optimization

Author : James C. Spall
Publisher : John Wiley & Sons
ISBN 13 : 0471441902
Total Pages : 620 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Introduction to Stochastic Search and Optimization by : James C. Spall

Download or read book Introduction to Stochastic Search and Optimization written by James C. Spall and published by John Wiley & Sons. This book was released on 2005-03-11 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Unique in its survey of the range of topics. * Contains a strong, interdisciplinary format that will appeal to both students and researchers. * Features exercises and web links to software and data sets.

Stochastic Recursive Algorithms for Optimization

Author : S. Bhatnagar
Publisher : Springer
ISBN 13 : 1447142853
Total Pages : 302 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Stochastic Recursive Algorithms for Optimization by : S. Bhatnagar

Download or read book Stochastic Recursive Algorithms for Optimization written by S. Bhatnagar and published by Springer. This book was released on 2012-08-11 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Optimization

Author : Kurt Marti
Publisher : Springer Science & Business Media
ISBN 13 : 3642882676
Total Pages : 189 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Stochastic Optimization by : Kurt Marti

Download or read book Stochastic Optimization written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes a selection of refereed papers presented at the GAMM/IFIP-Workshop on "Stochastic Optimization: Numerical Methods and Technical Applications", held at the Federal Armed Forces University Munich, May 29 - 31, 1990. The objective of this meeting was to bring together scientists from Stochastic Programming and from those Engineering areas, where Mathematical Programming models are common tools, as e. g. Optimal Structural Design, Power Dispatch, Acid Rain Management etc. The first, theoretical part includes the papers by S. D. Flam. H. Niederreiter, E. Poechinger and R. Schultz. The second part on methods and applications contains the articles by N. Baba, N. Grwe and W. Roemisch, J. Mayer, E. A. Mc Bean and A. Vasarhelyi.

Stochastic Simulation Optimization for Discrete Event Systems

Author : Chun-Hung Chen
Publisher : World Scientific
ISBN 13 : 9814513024
Total Pages : 274 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Stochastic Simulation Optimization for Discrete Event Systems by : Chun-Hung Chen

Download or read book Stochastic Simulation Optimization for Discrete Event Systems written by Chun-Hung Chen and published by World Scientific. This book was released on 2013-07-03 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete event systems (DES) have become pervasive in our daily lives. Examples include (but are not restricted to) manufacturing and supply chains, transportation, healthcare, call centers, and financial engineering. However, due to their complexities that often involve millions or even billions of events with many variables and constraints, modeling these stochastic simulations has long been a “hard nut to crack”. The advance in available computer technology, especially of cluster and cloud computing, has paved the way for the realization of a number of stochastic simulation optimization for complex discrete event systems. This book will introduce two important techniques initially proposed and developed by Professor Y C Ho and his team; namely perturbation analysis and ordinal optimization for stochastic simulation optimization, and present the state-of-the-art technology, and their future research directions. Contents:Part I: Perturbation Analysis:The IPA Calculus for Hybrid SystemsSmoothed Perturbation Analysis: A Retrospective and Prospective LookPerturbation Analysis and Variance Reduction in Monte Carlo SimulationAdjoints and AveragingInfinitesimal Perturbation Analysis and Optimization AlgorithmsSimulation-based Optimization of Failure-prone Continuous Flow LinesPerturbation Analysis, Dynamic Programming, and BeyondPart II: Ordinal Optimization:Fundamentals of Ordinal OptimizationOptimal Computing Budget Allocation FrameworkNested PartitionsApplications of Ordinal Optimization Readership: Professionals in industrial and systems engineering, graduate reference for probability & statistics, stochastic analysis and general computer science, and research. Keywords:Simulation;Optimization;Stochastic Systems;Discrete-Even Systems;Perturbation Analysis;Ordinal Optimization

Stochastic Optimization

Author : Vadim I. Arkin
Publisher : Springer
ISBN 13 :
Total Pages : 806 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Stochastic Optimization by : Vadim I. Arkin

Download or read book Stochastic Optimization written by Vadim I. Arkin and published by Springer. This book was released on 1986-06 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Approximation

Author : Vivek S. Borkar
Publisher : Springer
ISBN 13 : 938627938X
Total Pages : 177 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Stochastic Approximation by : Vivek S. Borkar

Download or read book Stochastic Approximation written by Vivek S. Borkar and published by Springer. This book was released on 2009-01-01 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Approximation and Recursive Algorithms and Applications

Author : Harold Kushner
Publisher : Springer Science & Business Media
ISBN 13 : 1489926968
Total Pages : 432 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Stochastic Approximation and Recursive Algorithms and Applications by : Harold Kushner

Download or read book Stochastic Approximation and Recursive Algorithms and Applications written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most comprehensive and thorough treatment of modern stochastic approximation type algorithms to date, based on powerful methods connected with that of the ODE. It covers general constrained and unconstrained problems, w.p.1 as well as the very successful weak convergence methods under weak conditions on the dynamics and noise processes, asymptotic properties and rates of convergence, iterate averaging methods, ergodic cost problems, state dependent noise, high dimensional problems, plus decentralized and asynchronous algorithms, and the use of methods of large deviations. Examples from many fields illustrate and motivate the techniques.

Random Iterative Models

Author : Marie Duflo
Publisher : Springer Science & Business Media
ISBN 13 : 3662128802
Total Pages : 394 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Random Iterative Models by : Marie Duflo

Download or read book Random Iterative Models written by Marie Duflo and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, self-contained review of a wide range of recursive methods for stabilization, identification and control of complex stochastic models (guiding a rocket or a plane, organizing multi-access broadcast channels, self-learning of neural networks ...). Suitable for mathematicians (researchers and also students) and engineers.

Stochastic Optimization Methods

Author : Kurt Marti
Publisher : Springer
ISBN 13 : 3662462141
Total Pages : 368 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Stochastic Optimization Methods by : Kurt Marti

Download or read book Stochastic Optimization Methods written by Kurt Marti and published by Springer. This book was released on 2015-02-21 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Filters

Author : Sueo Sugimoto
Publisher : Ohmsha, Ltd.
ISBN 13 : 4274805026
Total Pages : 457 pages
Book Rating : 4.2/5 (748 download)

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Book Synopsis Nonlinear Filters by : Sueo Sugimoto

Download or read book Nonlinear Filters written by Sueo Sugimoto and published by Ohmsha, Ltd.. This book was released on 2020-12-10 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method

Reinforcement Learning and Stochastic Optimization

Author : Warren B. Powell
Publisher : John Wiley & Sons
ISBN 13 : 1119815037
Total Pages : 1090 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Reinforcement Learning and Stochastic Optimization by : Warren B. Powell

Download or read book Reinforcement Learning and Stochastic Optimization written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2022-03-15 with total page 1090 pages. Available in PDF, EPUB and Kindle. Book excerpt: REINFORCEMENT LEARNING AND STOCHASTIC OPTIMIZATION Clearing the jungle of stochastic optimization Sequential decision problems, which consist of “decision, information, decision, information,” are ubiquitous, spanning virtually every human activity ranging from business applications, health (personal and public health, and medical decision making), energy, the sciences, all fields of engineering, finance, and e-commerce. The diversity of applications attracted the attention of at least 15 distinct fields of research, using eight distinct notational systems which produced a vast array of analytical tools. A byproduct is that powerful tools developed in one community may be unknown to other communities. Reinforcement Learning and Stochastic Optimization offers a single canonical framework that can model any sequential decision problem using five core components: state variables, decision variables, exogenous information variables, transition function, and objective function. This book highlights twelve types of uncertainty that might enter any model and pulls together the diverse set of methods for making decisions, known as policies, into four fundamental classes that span every method suggested in the academic literature or used in practice. Reinforcement Learning and Stochastic Optimization is the first book to provide a balanced treatment of the different methods for modeling and solving sequential decision problems, following the style used by most books on machine learning, optimization, and simulation. The presentation is designed for readers with a course in probability and statistics, and an interest in modeling and applications. Linear programming is occasionally used for specific problem classes. The book is designed for readers who are new to the field, as well as those with some background in optimization under uncertainty. Throughout this book, readers will find references to over 100 different applications, spanning pure learning problems, dynamic resource allocation problems, general state-dependent problems, and hybrid learning/resource allocation problems such as those that arose in the COVID pandemic. There are 370 exercises, organized into seven groups, ranging from review questions, modeling, computation, problem solving, theory, programming exercises and a “diary problem” that a reader chooses at the beginning of the book, and which is used as a basis for questions throughout the rest of the book.