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 e?cient 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 Neumann-Gale 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.
Reviews / Votes
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)
Series
Edition
1st ed. Softcover of orig. ed. 2006
Language
Place of publication
Target group
Professional and scholarly
Research
Illustrations
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 23 mm
Weight
ISBN-13
978-1-4419-3924-1 (9781441939241)
DOI
Schweitzer Classification
Simeon Reich is the Lord Leonard Wolfson Academic Chair and Professor of Mathematics at Technion-Israel Institute of Technology in Haifa. He has published more than fifty articles in mathematics journals including the Journal of Nonlinear Convex Analysis, SIAM Journal of Optimization, and Journal of Applied Analysis and fifteen books.
Alexander J. Zaslavski is a Senior Researcher in the Department of Mathematics at Technion-Israel Institute of Technology in Haifa. He has published over one hundred journal articles, and has authored books including Optimization on Metric and Normed Spaces (Springer, 2010) and Nonconvex Optimal Control and Variational Problems (Springer, 2013).
Infinite Horizon Variational Problems.- Extremals of Nonautonomous Problems.- Extremals of Autonomous Problems.- Infinite Horizon Autonomous Problems.- Turnpike for Autonomous Problems.- Linear Periodic Control Systems.- Linear Systems with Nonperiodic Integrands.- Discrete-Time Control Systems.- Control Problems in Hilbert Spaces.- A Class of Differential Inclusions.- Convex Processes.- A Dynamic Zero-Sum Game.
