Dynamic Optimization and Differential Games
Dynamic Optimization and Differential Games has been written to address the increasing number of Operations Research and Management Science problems that involve the explicit consideration of time and of gaming among multiple agents. With end-of-chapter e
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Volume 135
Series Editor Frederick S. Hillier Stanford University, CA, USA Special Editorial Consultant Camille C. Price Stephen F. Austin State University, TX, USA
For other titles published in this series, go to http://www.springer.com/series/6161
Terry L. Friesz
Dynamic Optimization and Differential Games
123
Terry L. Friesz Pennsylvania State University Dept. Industrial & Manufacturing Engineering 305 Leonhard Building University Park, Pennsylvania 16802 USA [email protected]
ISBN 978-0-387-72777-6 e-ISBN 978-0-387-72778-3 DOI 10.1007/978-0-387-72778-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010933511 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
Preface .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . xiii 1
Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.1 Brief History of the Calculus of Variations and Optimal Control .. . . 1.2 The Brachistochrone Problem . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.3 Optimal Economic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.3.1 Ramsey’s 1928 Model .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.3.2 Neoclassical Optimal Growth .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.4 Regional Allocation of Public Investment . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.4.1 The Dynamics of Capital Formation.. . . . . . .. . . . . . . . . . . . . . . . . 1.4.2 Population Dynamics .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.4.3 Technological Change .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.4.4 Criterion Functional and Final Form of the Model . . . . . . . . . 1.5 Dynamic Telecommunications Flow Routing.. . . . . . .. . . . . . . . . . . . . . . . . 1.5.1 Assumptions and Notation . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1.5.2 Flow Propagation Mechanism . . . .
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