Turnpike Properties in the Calculus of Variations and Optimal Control / Edition 1

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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.

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Editorial Reviews

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"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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Product Details

Table of Contents

1 Infinite horizon variational problems 1
2 Extremals of nonautonomous problems 33
3 Extremals of autonomous problems 71
4 Infinite horizon autonomous problems 115
5 Turnpike for autonomous problems 153
6 Linear periodic control systems 173
7 Linear systems with nonperiodic integrands 197
8 Discrete-time control systems 223
9 Control problems in Hilbert spaces 257
10 A class of differential inclusions 283
11 Convex processes 321
12 A dynamic zero-sum game 349
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