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Author: A.B. Piunovskiy
Publisher: Springer Science & Business Media
ISBN: 9401155089
Category : Mathematics
Languages : en
Pages : 355
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Book Description
Controlled stochastic processes with discrete time form a very interest ing and meaningful field of research which attracts widespread attention. At the same time these processes are used for solving of many applied problems in the queueing theory, in mathematical economics. in the theory of controlled technical systems, etc. . In this connection, methods of the theory of controlled processes constitute the every day instrument of many specialists working in the areas mentioned. The present book is devoted to the rather new area, that is, to the optimal control theory with functional constraints. This theory is close to the theory of multicriteria optimization. The compromise between the mathematical rigor and the big number of meaningful examples makes the book attractive for professional mathematicians and for specialists who ap ply mathematical methods in different specific problems. Besides. the book contains setting of many new interesting problems for further invf'stigatioll. The book can form the basis of special courses in the theory of controlled stochastic processes for students and post-graduates specializing in the ap plied mathematics and in the control theory of complex systf'ms. The grounding of graduating students of mathematical department is sufficient for the perfect understanding of all the material. The book con tains the extensive Appendix where the necessary knowledge ill Borel spaces and in convex analysis is collected. All the meaningful examples can be also understood by readers who are not deeply grounded in mathematics.
Author: A.B. Piunovskiy
Publisher: Springer Science & Business Media
ISBN: 9401155089
Category : Mathematics
Languages : en
Pages : 355
Get Book Here
Book Description
Controlled stochastic processes with discrete time form a very interest ing and meaningful field of research which attracts widespread attention. At the same time these processes are used for solving of many applied problems in the queueing theory, in mathematical economics. in the theory of controlled technical systems, etc. . In this connection, methods of the theory of controlled processes constitute the every day instrument of many specialists working in the areas mentioned. The present book is devoted to the rather new area, that is, to the optimal control theory with functional constraints. This theory is close to the theory of multicriteria optimization. The compromise between the mathematical rigor and the big number of meaningful examples makes the book attractive for professional mathematicians and for specialists who ap ply mathematical methods in different specific problems. Besides. the book contains setting of many new interesting problems for further invf'stigatioll. The book can form the basis of special courses in the theory of controlled stochastic processes for students and post-graduates specializing in the ap plied mathematics and in the control theory of complex systf'ms. The grounding of graduating students of mathematical department is sufficient for the perfect understanding of all the material. The book con tains the extensive Appendix where the necessary knowledge ill Borel spaces and in convex analysis is collected. All the meaningful examples can be also understood by readers who are not deeply grounded in mathematics.
Author: A.B. Piunovskiy
Publisher: Springer
ISBN: 9789401155090
Category : Mathematics
Languages : en
Pages : 348
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Book Description
Controlled stochastic processes with discrete time form a very interest ing and meaningful field of research which attracts widespread attention. At the same time these processes are used for solving of many applied problems in the queueing theory, in mathematical economics. in the theory of controlled technical systems, etc. . In this connection, methods of the theory of controlled processes constitute the every day instrument of many specialists working in the areas mentioned. The present book is devoted to the rather new area, that is, to the optimal control theory with functional constraints. This theory is close to the theory of multicriteria optimization. The compromise between the mathematical rigor and the big number of meaningful examples makes the book attractive for professional mathematicians and for specialists who ap ply mathematical methods in different specific problems. Besides. the book contains setting of many new interesting problems for further invf'stigatioll. The book can form the basis of special courses in the theory of controlled stochastic processes for students and post-graduates specializing in the ap plied mathematics and in the control theory of complex systf'ms. The grounding of graduating students of mathematical department is sufficient for the perfect understanding of all the material. The book con tains the extensive Appendix where the necessary knowledge ill Borel spaces and in convex analysis is collected. All the meaningful examples can be also understood by readers who are not deeply grounded in mathematics.
Author: Eitan Altman
Publisher: CRC Press
ISBN: 9780849303821
Category : Mathematics
Languages : en
Pages : 260
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Book Description
This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields. A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other. The first part explains the theory for the finite state space. The author characterizes the set of achievable expected occupation measures as well as performance vectors, and identifies simple classes of policies among which optimal policies exist. This allows the reduction of the original dynamic into a linear program. A Lagranian approach is then used to derive the dual linear program using dynamic programming techniques. In the second part, these results are extended to the infinite state space and action spaces. The author provides two frameworks: the case where costs are bounded below and the contracting framework. The third part builds upon the results of the first two parts and examines asymptotical results of the convergence of both the value and the policies in the time horizon and in the discount factor. Finally, several state truncation algorithms that enable the approximation of the solution of the original control problem via finite linear programs are given.
Author: Nicole Bäuerle
Publisher: Springer Science & Business Media
ISBN: 3642183247
Category : Mathematics
Languages : en
Pages : 393
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Book Description
The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and at the same time show its application by means of numerous examples, mostly taken from the fields of finance and operations research. By using a structural approach many technicalities (concerning measure theory) are avoided. They cover problems with finite and infinite horizons, as well as partially observable Markov decision processes, piecewise deterministic Markov decision processes and stopping problems. The book presents Markov decision processes in action and includes various state-of-the-art applications with a particular view towards finance. It is useful for upper-level undergraduates, Master's students and researchers in both applied probability and finance, and provides exercises (without solutions).
Author: Eugene A. Feinberg
Publisher: Springer Science & Business Media
ISBN: 1461508053
Category : Business & Economics
Languages : en
Pages : 560
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Book Description
Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation.
Author: Alexei A. Gaivoronski
Publisher: CRC Press
ISBN: 1000983927
Category : Computers
Languages : en
Pages : 388
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Book Description
The book comprises original articles on topical issues of risk theory, rational decision making, statistical decisions, and control of stochastic systems. The articles are the outcome of a series international projects involving the leading scholars in the field of modern stochastic optimization and decision making. The structure of stochastic optimization solvers is described. The solvers in general implement stochastic quasi-gradient methods for optimization and identification of complex nonlinear models. These models constitute an important methodology for finding optimal decisions under risk and uncertainty. While a large part of current approaches towards optimization under uncertainty stems from linear programming (LP) and often results in large LPs of special structure, stochastic quasi-gradient methods confront nonlinearities directly without need of linearization. This makes them an appropriate tool for solving complex nonlinear problems, concurrent optimization and simulation models, and equilibrium situations of different types, for instance, Nash or Stackelberg equilibrium situations. The solver finds the equilibrium solution when the optimization model describes the system with several actors. The solver is parallelizable, performing several simulation threads in parallel. It is capable of solving stochastic optimization problems, finding stochastic Nash equilibria, and of composite stochastic bilevel problems where each level may require the solution of stochastic optimization problem or finding Nash equilibrium. Several complex examples with applications to water resources management, energy markets, pricing of services on social networks are provided. In the case of power system, regulator makes decision on the final expansion plan, considering the strategic behavior of regulated companies and coordinating the interests of different economic entities. Such a plan can be an equilibrium − a planned decision where a company cannot increase its expected gain unilaterally.
Author: Alexey Piunovskiy
Publisher: Springer Nature
ISBN: 3030549879
Category : Mathematics
Languages : en
Pages : 605
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Book Description
This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.
Author: Tomas Prieto-rumeau
Publisher: World Scientific
ISBN: 1908977639
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas.An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown.This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.
Author: Andrey Sarychev
Publisher: Springer Science & Business Media
ISBN: 354069532X
Category : Mathematics
Languages : en
Pages : 418
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Book Description
Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.
Author: Sabine Mondie
Publisher: Elsevier
ISBN: 9780080441313
Category : Science
Languages : en
Pages : 780
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Book Description
