Optimization Under Stochastic Uncertainty

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Stochastic Optimization Methods

Author : Kurt Marti
Publisher : Springer
ISBN 13 : 3662462141
Total Pages : 389 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 389 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.

Introduction to Applied Optimization

Author : Urmila Diwekar
Publisher : Springer Science & Business Media
ISBN 13 : 1475737459
Total Pages : 342 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Applied Optimization by : Urmila Diwekar

Download or read book Introduction to Applied Optimization written by Urmila Diwekar and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter. Introduction to Applied Optimization is intended for advanced undergraduate and graduate students and will benefit scientists from diverse areas, including engineers.

Optimization Under Stochastic Uncertainty

Author : Kurt Marti
Publisher : Springer Nature
ISBN 13 : 303055662X
Total Pages : 390 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Optimization Under Stochastic Uncertainty by : Kurt Marti

Download or read book Optimization Under Stochastic Uncertainty written by Kurt Marti and published by Springer Nature. This book was released on 2020-11-10 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines application and methods to incorporating stochastic parameter variations into the optimization process to decrease expense in corrective measures. Basic types of deterministic substitute problems occurring mostly in practice involve i) minimization of the expected primary costs subject to expected recourse cost constraints (reliability constraints) and remaining deterministic constraints, e.g. box constraints, as well as ii) minimization of the expected total costs (costs of construction, design, recourse costs, etc.) subject to the remaining deterministic constraints. After an introduction into the theory of dynamic control systems with random parameters, the major control laws are described, as open-loop control, closed-loop, feedback control and open-loop feedback control, used for iterative construction of feedback controls. For approximate solution of optimization and control problems with random parameters and involving expected cost/loss-type objective, constraint functions, Taylor expansion procedures, and Homotopy methods are considered, Examples and applications to stochastic optimization of regulators are given. Moreover, for reliability-based analysis and optimal design problems, corresponding optimization-based limit state functions are constructed. Because of the complexity of concrete optimization/control problems and their lack of the mathematical regularity as required of Mathematical Programming (MP) techniques, other optimization techniques, like random search methods (RSM) became increasingly important. Basic results on the convergence and convergence rates of random search methods are presented. Moreover, for the improvement of the – sometimes very low – convergence rate of RSM, search methods based on optimal stochastic decision processes are presented. In order to improve the convergence behavior of RSM, the random search procedure is embedded into a stochastic decision process for an optimal control of the probability distributions of the search variates (mutation random variables).

Stochastic Optimization Methods

Author : Kurt Marti
Publisher : Springer Science & Business Media
ISBN 13 : 3540268480
Total Pages : 317 pages
Book Rating : 4.5/5 (42 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 Science & Business Media. This book was released on 2005-12-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Optimization Techniques for Problem Solving in Uncertainty

Author : Tilahun, Surafel Luleseged
Publisher : IGI Global
ISBN 13 : 1522550925
Total Pages : 327 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis Optimization Techniques for Problem Solving in Uncertainty by : Tilahun, Surafel Luleseged

Download or read book Optimization Techniques for Problem Solving in Uncertainty written by Tilahun, Surafel Luleseged and published by IGI Global. This book was released on 2018-06-22 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: When it comes to optimization techniques, in some cases, the available information from real models may not be enough to construct either a probability distribution or a membership function for problem solving. In such cases, there are various theories that can be used to quantify the uncertain aspects. Optimization Techniques for Problem Solving in Uncertainty is a scholarly reference resource that looks at uncertain aspects involved in different disciplines and applications. Featuring coverage on a wide range of topics including uncertain preference, fuzzy multilevel programming, and metaheuristic applications, this book is geared towards engineers, managers, researchers, and post-graduate students seeking emerging research in the field of optimization.

Convex and Stochastic Optimization

Author : J. Frédéric Bonnans
Publisher : Springer
ISBN 13 : 3030149773
Total Pages : 320 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Convex and Stochastic Optimization by : J. Frédéric Bonnans

Download or read book Convex and Stochastic Optimization written by J. Frédéric Bonnans and published by Springer. This book was released on 2019-04-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Programming

Author : Willem K. Klein Haneveld
Publisher : Springer Nature
ISBN 13 : 3030292193
Total Pages : 255 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Stochastic Programming by : Willem K. Klein Haneveld

Download or read book Stochastic Programming written by Willem K. Klein Haneveld and published by Springer Nature. This book was released on 2019-10-24 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multistage Stochastic Optimization

Author : Georg Ch. Pflug
Publisher : Springer
ISBN 13 : 3319088432
Total Pages : 309 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Multistage Stochastic Optimization by : Georg Ch. Pflug

Download or read book Multistage Stochastic Optimization written by Georg Ch. Pflug and published by Springer. This book was released on 2014-11-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Stochastic Programming

Author : John R. Birge
Publisher : Springer Science & Business Media
ISBN 13 : 0387226184
Total Pages : 427 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Stochastic Programming by : John R. Birge

Download or read book Introduction to Stochastic Programming written by John R. Birge and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Lectures on Stochastic Programming

Author : Alexander Shapiro
Publisher : SIAM
ISBN 13 : 0898718759
Total Pages : 447 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Stochastic Programming by : Alexander Shapiro

Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2009-01-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Robust Optimization

Author : Aharon Ben-Tal
Publisher : Princeton University Press
ISBN 13 : 1400831059
Total Pages : 565 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Robust Optimization by : Aharon Ben-Tal

Download or read book Robust Optimization written by Aharon Ben-Tal and published by Princeton University Press. This book was released on 2009-08-10 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Handbook of Smart Cities

Author : Juan Carlos Augusto
Publisher : Springer
ISBN 13 : 9783030696979
Total Pages : 1697 pages
Book Rating : 4.6/5 (969 download)

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Book Synopsis Handbook of Smart Cities by : Juan Carlos Augusto

Download or read book Handbook of Smart Cities written by Juan Carlos Augusto and published by Springer. This book was released on 2021-07-17 with total page 1697 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook presents a comprehensive and rigorous overview of the state-of-the-art on Smart Cities. It provides the reader with an authoritative, exhaustive one-stop reference on how the field has evolved and where the current and future challenges lie. From the foundations to the many overlapping dimensions (human, energy, technology, data, institutions, ethics etc.), each chapter is written by international experts and amply illustrated with figures and tables with an emphasis on current research. The Handbook is an invaluable desk reference for researchers in a wide variety of fields, not only smart cities specialists but also by scientists and policy-makers in related disciplines that are deeply influenced by the emergence of intelligent cities. It should also serve as a key resource for graduate students and young researchers entering the area, and for instructors who teach courses on these subjects. The handbook is also of interest to industry and business innovators.

Dynamic Stochastic Optimization

Author : Kurt Marti
Publisher : Springer Science & Business Media
ISBN 13 : 9783540405061
Total Pages : 348 pages
Book Rating : 4.4/5 (5 download)

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Book Synopsis Dynamic Stochastic Optimization by : Kurt Marti

Download or read book Dynamic Stochastic Optimization written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2004 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers optimal stochastic decision processes from the viewpoint of stochastic programming. It focuses on theoretical properties and on approximate or numerical solution techniques for time-dependent optimization problems with random parameters (multistage stochastic programs, optimal stochastic decision processes). Methods for finding approximate solutions of probabilistic and expected cost based deterministic substitute problems are presented. Besides theoretical and numerical considerations, the proceedings volume contains selected refereed papers on many practical applications to economics and engineering: risk, risk management, portfolio management, finance, insurance-matters and control of robots.

Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Author : Harald Held
Publisher : Springer Science & Business Media
ISBN 13 : 383489396X
Total Pages : 140 pages
Book Rating : 4.8/5 (348 download)

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Book Synopsis Shape Optimization under Uncertainty from a Stochastic Programming Point of View by : Harald Held

Download or read book Shape Optimization under Uncertainty from a Stochastic Programming Point of View written by Harald Held and published by Springer Science & Business Media. This book was released on 2010-05-30 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.

Stochastic Optimization

Author : Ioannis Dritsas
Publisher : IntechOpen
ISBN 13 : 9789533078298
Total Pages : 490 pages
Book Rating : 4.0/5 (782 download)

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Book Synopsis Stochastic Optimization by : Ioannis Dritsas

Download or read book Stochastic Optimization written by Ioannis Dritsas and published by IntechOpen. This book was released on 2011-02-28 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Optimization Algorithms have become essential tools in solving a wide range of difficult and critical optimization problems. Such methods are able to find the optimum solution of a problem with uncertain elements or to algorithmically incorporate uncertainty to solve a deterministic problem. They even succeed in fighting uncertainty with uncertainty. This book discusses theoretical aspects of many such algorithms and covers their application in various scientific fields.

Stochastic Optimization Models in Finance

Author : William T. Ziemba
Publisher : World Scientific
ISBN 13 : 981256800X
Total Pages : 756 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Stochastic Optimization Models in Finance by : William T. Ziemba

Download or read book Stochastic Optimization Models in Finance written by William T. Ziemba and published by World Scientific. This book was released on 2006 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.