Author: Julio B. Clempner
Publisher: Springer Nature
ISBN: 3031435753
Category : Technology & Engineering
Languages : en
Pages : 340
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Book Description
This book considers a class of ergodic finite controllable Markov's chains. The main idea behind the method, described in this book, is to develop the original discrete optimization problems (or game models) in the space of randomized formulations, where the variables stand in for the distributions (mixed strategies or preferences) of the original discrete (pure) strategies in the use. The following suppositions are made: a finite state space, a limited action space, continuity of the probabilities and rewards associated with the actions, and a necessity for accessibility. These hypotheses lead to the existence of an optimal policy. The best course of action is always stationary. It is either simple (i.e., nonrandomized stationary) or composed of two nonrandomized policies, which is equivalent to randomly selecting one of two simple policies throughout each epoch by tossing a biased coin. As a bonus, the optimization procedure just has to repeatedly solve the time-average dynamic programming equation, making it theoretically feasible to choose the optimum course of action under the global restriction. In the ergodic cases the state distributions, generated by the corresponding transition equations, exponentially quickly converge to their stationary (final) values. This makes it possible to employ all widely used optimization methods (such as Gradient-like procedures, Extra-proximal method, Lagrange's multipliers, Tikhonov's regularization), including the related numerical techniques. In the book we tackle different problems and theoretical Markov models like controllable and ergodic Markov chains, multi-objective Pareto front solutions, partially observable Markov chains, continuous-time Markov chains, Nash equilibrium and Stackelberg equilibrium, Lyapunov-like function in Markov chains, Best-reply strategy, Bayesian incentive-compatible mechanisms, Bayesian Partially Observable Markov Games, bargaining solutions for Nash and Kalai-Smorodinsky formulations, multi-traffic signal-control synchronization problem, Rubinstein's non-cooperative bargaining solutions, the transfer pricing problem as bargaining.
Author: Daniel Hernández-Hernández
Publisher: Springer Science & Business Media
ISBN: 0817683372
Category : Science
Languages : en
Pages : 331
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Book Description
This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.
Author: Wendell H. Fleming
Publisher: Springer Science & Business Media
ISBN: 0387310711
Category : Mathematics
Languages : en
Pages : 436
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Book Description
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
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: Society for Industrial and Applied Mathematics
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 1136
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Book Description
Author: Samson Lasaulce
Publisher: Birkhäuser
ISBN: 3319510347
Category : Mathematics
Languages : en
Pages : 237
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Book Description
This contributed volume offers a collection of papers presented at the 2016 Network Games, Control, and Optimization conference (NETGCOOP), held at the University of Avignon in France, November 23-25, 2016. These papers highlight the increasing importance of network control and optimization in many networking application domains, such as mobile and fixed access networks, computer networks, social networks, transportation networks, and, more recently, electricity grids and biological networks. Covering a wide variety of both theoretical and applied topics in the areas listed above, the authors explore several conceptual and algorithmic tools that are needed for efficient and robust control operation, performance optimization, and better understanding the relationships between entities that may be acting cooperatively or selfishly in uncertain and possibly adversarial environments. As such, this volume will be of interest to applied mathematicians, computer scientists, engineers, and researchers in other related fields.
Author: Dmitrii Lozovanu
Publisher: Springer
ISBN: 3319118331
Category : Business & Economics
Languages : en
Pages : 420
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Book Description
This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book’s final chapter is devoted to finite horizon stochastic control problems and Markov decision processes. The algorithms developed represent a valuable contribution to the important field of computational network theory.
Author: Zhenting Hou
Publisher: Springer Science & Business Media
ISBN: 146130265X
Category : Mathematics
Languages : en
Pages : 501
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Book Description
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South American and Asian scholars.
Author: Kandethody M. Ramachandran
Publisher: Springer Science & Business Media
ISBN: 9491216473
Category : Mathematics
Languages : en
Pages : 253
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Book Description
The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.
Author: Xianping Guo
Publisher: Springer Science & Business Media
ISBN: 3642025471
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.
