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Turnpike Properties in the Calculus of Variations and Optimal Control

Alexander Zaslavski

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ISBN 10: 1441939245 / ISBN 13: 9781441939241
Published by Springer
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396 pages. Dimensions: 9.0in. x 6.0in. x 0.9in.This monograph is devoted to recent progress in the turnpike t- ory. Turnpike properties are well known in mathematical economics. The term was rst coined by Samuelson who showed that an ecient expanding economy would for most of the time be in the vicinity of a balanced equilibrium path (also called a von Neumann path) 78, 79. These properties were studied by many authors for optimal trajec- ries of a NeumannGale model determined by a superlinear set-valued mapping. In the monograph we discuss a number of results conce- ing turnpike properties in the calculus of variations and optimal control which were obtained by the author in the last ten years. These results showthattheturnpikepropertiesareageneralphenomenonwhichholds for various classes of variational problems and optimal control problems. Turnpike properties are studied for optimal control problems on- nite time intervals T , T of the real line. Solutions of such problems 1 2 (trajectories) always depend on the time interval T , T , an optimality 1 2 criterion which is usually determined by a cost function, and on data which is some initial conditions. In the turnpike theory we are int- ested in the structure of solutions of optimal problems. We study the behavior of solutions when an optimality criterion is xed while T , T 1 2 andthedatavary. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9781441939241

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Bibliographic Details

Title: Turnpike Properties in the Calculus of ...

Publisher: Springer

Binding: Paperback

Book Condition:New

Book Type: Paperback

About this title


This book is devoted to the recent progress on the turnpike theory. The turnpike property was discovered by Paul A. Samuelson, who applied it to problems in mathematical economics in 1949. These properties were studied for optimal trajectories of models of economic dynamics determined by convex processes. In this monograph the author, a leading expert in modern turnpike theory, presents a number of results concerning the turnpike properties in the calculus of variations and optimal control which were obtained in the last ten years. These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems. The book should help to correct the misapprehension that turnpike properties are only special features of some narrow classes of convex problems of mathematical economics.


From the reviews:

"The book is a compilation of the intensive work of the author on the turnpike property over the past 10 to 15 years ... . The book should be of interest not only to researchers in mathematical economics but also to those in optimal control theory and the calculus of variations whose interests lie in the structural properties of the long term behavior of optimal solutions." (Dean A. Carlson, Mathematical Reviews, Issue 2006 f)

"This monograph is dedicated to the study of the turnpike theory and is based mainly on the author’s results on the subject obtained in the last twenty years. ... The list of references has 112 items, 23 being papers of the author. It also contains a preface, an introduction and an index. The book addresses to mathematicians working in optimal control, calculus of variations, mathematical economics and game theory." (Constantin Zalinescu, Zentralblatt MATH, Vol. 1100 (2), 2007)

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