Optimization of Stochastic Systems

Optimization of Stochastic Systems PDF

Author: Masanao Aoki

Publisher: Academic Press

Published: 1967-01-01

Total Pages: 374

ISBN-13: 0080955398

DOWNLOAD EBOOK →

Optimization of Stochastic Systems is an outgrowth of class notes of a graduate level seminar on optimization of stochastic systems. Most of the material in the book was taught for the first time during the 1965 Spring Semester while the author was visiting the Department of Electrical Engineering, University of California, Berkeley. The revised and expanded material was presented at the Department of Engineering, University of California, Los Angeles during the 1965 Fall Semester. The systems discussed in the book are mostly assumed to be of discrete-time type with continuous state variables taking values in some subsets of Euclidean spaces. There is another class of systems in which state variables are assumed to take on at most a denumerable number of values, i.e., these systems are of discrete-time discrete-space type. Although the problems associated with the latter class of systems are many and interesting, andalthough they are amenable to deep analysis on such topics as the limiting behaviors of state variables as time indexes increase to infinity, this class of systems is not included here, partly because there are many excellent books on the subjects and partly because inclusion of these materials would easily double the size of the book.

Stochastic Approximation and Optimization of Random Systems

Stochastic Approximation and Optimization of Random Systems PDF

Author: L. Ljung

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 120

ISBN-13: 3034886098

DOWNLOAD EBOOK →

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 Simulation Optimization for Discrete Event Systems

Stochastic Simulation Optimization for Discrete Event Systems PDF

Author: Chun-Hung Chen

Publisher: World Scientific

Published: 2013-07-03

Total Pages: 274

ISBN-13: 9814513024

DOWNLOAD EBOOK →

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 Methods

Stochastic Optimization Methods PDF

Author: Kurt Marti

Publisher: Springer

Published: 2015-02-21

Total Pages: 389

ISBN-13: 3662462141

DOWNLOAD EBOOK →

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.

Stochastic Multi-Stage Optimization

Stochastic Multi-Stage Optimization PDF

Author: Pierre Carpentier

Publisher: Springer

Published: 2015-05-05

Total Pages: 362

ISBN-13: 3319181386

DOWNLOAD EBOOK →

The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.

Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems

Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems PDF

Author: Houmin Yan

Publisher: Springer Science & Business Media

Published: 2006-09-10

Total Pages: 397

ISBN-13: 0387338152

DOWNLOAD EBOOK →

This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.

Stochastic Simulation Optimization

Stochastic Simulation Optimization PDF

Author: Chun-hung Chen

Publisher: World Scientific

Published: 2011

Total Pages: 246

ISBN-13: 9814282642

DOWNLOAD EBOOK →

With the advance of new computing technology, simulation is becoming very popular for designing large, complex and stochastic engineering systems, since closed-form analytical solutions generally do not exist for such problems. However, the added flexibility of simulation often creates models that are computationally intractable. Moreover, to obtain a sound statistical estimate at a specified level of confidence, a large number of simulation runs (or replications) is usually required for each design alternative. If the number of design alternatives is large, the total simulation cost can be very expensive. Stochastic Simulation Optimization addresses the pertinent efficiency issue via smart allocation of computing resource in the simulation experiments for optimization, and aims to provide academic researchers and industrial practitioners with a comprehensive coverage of OCBA approach for stochastic simulation optimization. Starting with an intuitive explanation of computing budget allocation and a discussion of its impact on optimization performance, a series of OCBA approaches developed for various problems are then presented, from the selection of the best design to optimization with multiple objectives. Finally, this book discusses the potential extension of OCBA notion to different applications such as data envelopment analysis, experiments of design and rare-event simulation.

Continuous-time Stochastic Control and Optimization with Financial Applications

Continuous-time Stochastic Control and Optimization with Financial Applications PDF

Author: Huyên Pham

Publisher: Springer Science & Business Media

Published: 2009-05-28

Total Pages: 243

ISBN-13: 3540895000

DOWNLOAD EBOOK →

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.