Stochastic Programming

Author : John R. Birge,François Louveaux
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 43,5 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226187

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Introduction to Stochastic Programming by John R. Birge,François Louveaux Pdf

This rapidly developing field encompasses many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors present a broad overview of the main themes and methods of the subject, thus helping students develop an intuition for how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The early chapters introduce some worked examples of stochastic programming, demonstrate how a stochastic model is formally built, develop the properties of stochastic programs and the basic solution techniques used to solve them. The book then goes on to cover approximation and sampling techniques and is rounded off by an in-depth case study. A well-paced and wide-ranging introduction to this subject.

Author : Alexander Shapiro,Darinka Dentcheva,Andrzej Ruszczy?ski
Publisher : SIAM
Page : 447 pages
File Size : 43,6 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898718751

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Lectures on Stochastic Programming by Alexander Shapiro,Darinka Dentcheva,Andrzej Ruszczy?ski Pdf

Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.

Author : Alan J. King,Stein W. Wallace
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 54,9 Mb
Release : 2012-06-19
Category : Mathematics
ISBN : 9780387878171

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Modeling with Stochastic Programming by Alan J. King,Stein W. Wallace Pdf

While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research at Lancaster University Management School in England.

Author : András Prékopa,Roger J.-B. Wets
Publisher : Unknown
Page : 196 pages
File Size : 53,9 Mb
Release : 1986
Category : Stochastic programming
ISBN : STANFORD:36105002029812

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Stochastic Programming 84 by András Prékopa,Roger J.-B. Wets Pdf

Author : Sheldon M. Ross
Publisher : Academic Press
Page : 178 pages
File Size : 41,5 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483269092

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Introduction to Stochastic Dynamic Programming by Sheldon M. Ross Pdf

Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.

Author : Willem K. Klein Haneveld,Maarten H. van der Vlerk,Ward Romeijnders
Publisher : Springer Nature
Page : 249 pages
File Size : 42,6 Mb
Release : 2019-10-24
Category : Business & Economics
ISBN : 9783030292195

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Stochastic Programming by Willem K. Klein Haneveld,Maarten H. van der Vlerk,Ward Romeijnders Pdf

This book provides an essential introduction to Stochastic Programming, especially intended for graduate students. The book begins by exploring a linear programming problem with random parameters, representing a decision problem under uncertainty. Several models for this problem are presented, including the main ones used in Stochastic Programming: recourse models and chance constraint models. The book not only discusses the theoretical properties of these models and algorithms for solving them, but also explains the intrinsic differences between the models. In the book’s closing section, several case studies are presented, helping students apply the theory covered to practical problems. The book is based on lecture notes developed for an Econometrics and Operations Research course for master students at the University of Groningen, the Netherlands - the longest-standing Stochastic Programming course worldwide.

Author : William T. Ziemba,Raymond G. Vickson
Publisher : World Scientific
Page : 756 pages
File Size : 48,8 Mb
Release : 2006
Category : Business & Economics
ISBN : 9789812568007

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Stochastic Optimization Models in Finance by William T. Ziemba,Raymond G. Vickson Pdf

A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems.Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever.

Author : Pierre Carpentier,Jean-Philippe Chancelier,Guy Cohen,Michel De Lara
Publisher : Springer
Page : 362 pages
File Size : 41,8 Mb
Release : 2015-05-05
Category : Mathematics
ISBN : 9783319181387

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Stochastic Multi-Stage Optimization by Pierre Carpentier,Jean-Philippe Chancelier,Guy Cohen,Michel De Lara Pdf

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.

Author : Johannes Schneider,Scott Kirkpatrick
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 52,8 Mb
Release : 2007-08-06
Category : Computers
ISBN : 9783540345602

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Stochastic Optimization by Johannes Schneider,Scott Kirkpatrick Pdf

This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.

Author : Warren B. Powell
Publisher : John Wiley & Sons
Page : 1090 pages
File Size : 48,9 Mb
Release : 2022-03-15
Category : Mathematics
ISBN : 9781119815037

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Reinforcement Learning and Stochastic Optimization by Warren B. Powell Pdf

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.

Author : Gerd Infanger
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 52,5 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 9781441916426

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Stochastic Programming by Gerd Infanger Pdf

From the Preface... The preparation of this book started in 2004, when George B. Dantzig and I, following a long-standing invitation by Fred Hillier to contribute a volume to his International Series in Operations Research and Management Science, decided finally to go ahead with editing a volume on stochastic programming. The field of stochastic programming (also referred to as optimization under uncertainty or planning under uncertainty) had advanced significantly in the last two decades, both theoretically and in practice. George Dantzig and I felt that it would be valuable to showcase some of these advances and to present what one might call the state-of- the-art of the field to a broader audience. We invited researchers whom we considered to be leading experts in various specialties of the field, including a few representatives of promising developments in the making, to write a chapter for the volume. Unfortunately, to the great loss of all of us, George Dantzig passed away on May 13, 2005. Encouraged by many colleagues, I decided to continue with the book and edit it as a volume dedicated to George Dantzig. Management Science published in 2005 a special volume featuring the “Ten most Influential Papers of the first 50 Years of Management Science.” George Dantzig’s original 1955 stochastic programming paper, “Linear Programming under Uncertainty,” was featured among these ten. Hearing about this, George Dantzig suggested that his 1955 paper be the first chapter of this book. The vision expressed in that paper gives an important scientific and historical perspective to the book. Gerd Infanger

Author : Georg Ch. Pflug,Alois Pichler
Publisher : Springer
Page : 301 pages
File Size : 42,6 Mb
Release : 2014-11-12
Category : Business & Economics
ISBN : 9783319088433

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Multistage Stochastic Optimization by Georg Ch. Pflug,Alois Pichler Pdf

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.

Author : Peter Kall,János Mayer
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 42,6 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9781441977298

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Stochastic Linear Programming by Peter Kall,János Mayer Pdf

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. ... The presentation includes geometric interpretation, linear programming duality, and the simplex method in its primal and dual forms. ... The authors have made an effort to collect ... the most useful recent ideas and algorithms in this area. ... A guide to the existing software is included as well." (Darinka Dentcheva, Mathematical Reviews, Issue 2006 c) "This is a graduate text in optimisation whose main emphasis is in stochastic programming. The book is clearly written. ... This is a good book for providing mathematicians, economists and engineers with an almost complete start up information for working in the field. I heartily welcome its publication. ... It is evident that this book will constitute an obligatory reference source for the specialists of the field." (Carlos Narciso Bouza Herrera, Zentralblatt MATH, Vol. 1104 (6), 2007)

Author : J. Frédéric Bonnans
Publisher : Springer
Page : 311 pages
File Size : 51,5 Mb
Release : 2019-04-24
Category : Mathematics
ISBN : 9783030149772

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Convex and Stochastic Optimization by J. Frédéric Bonnans Pdf

This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules. This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.

Author : Alexander Shapiro,Darinka Dentcheva,Andrzej Ruszczy?ski
Publisher : SIAM
Page : 494 pages
File Size : 49,5 Mb
Release : 2014-07-09
Category : Mathematics
ISBN : 9781611973433

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Lectures on Stochastic Programming by Alexander Shapiro,Darinka Dentcheva,Andrzej Ruszczy?ski Pdf

Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. In Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results.