Nonconvex Optimization and Its Applications

Turnpike Properties in the Calculus of Variations and Optimal Control

Authors: Zaslavski, Alexander J.

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About this book

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.

 

Audience

This book is intended for mathematicians interested in optimal control, calculus of variations, game theory and mathematical economics.

Reviews

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)


Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-0-387-28154-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-0-387-28155-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4419-3924-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Turnpike Properties in the Calculus of Variations and Optimal Control
Authors
Series Title
Nonconvex Optimization and Its Applications
Series Volume
80
Copyright
2006
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-28154-4
DOI
10.1007/0-387-28154-1
Hardcover ISBN
978-0-387-28155-1
Softcover ISBN
978-1-4419-3924-1
Series ISSN
1571-568X
Edition Number
1
Number of Pages
XXII, 396
Topics