About this book
Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems.
Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with “good” functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author.
This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community.
Also by Alexander J. Zaslavski: Optimization on Metric and Normed Spaces, © 2010; Structure of Solutions of Variational Problems, © 2013; Turnpike Properties in the Calculus of Variations and Optimal Control, © 2006.
- Book Title Nonconvex Optimal Control and Variational Problems
- Series Title Springer Optimization and Its Applications
- Series Abbreviated Title Springer Optimization
- DOI https://doi.org/10.1007/978-1-4614-7378-7
- Copyright Information Springer Science+Business Media New York 2013
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-1-4614-7377-0
- Softcover ISBN 978-1-4899-9622-0
- eBook ISBN 978-1-4614-7378-7
- Series ISSN 1931-6828
- Edition Number 1
- Number of Pages XI, 378
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Calculus of Variations and Optimal Control; Optimization
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From the reviews:“This monograph gives a well presented treatment of nonconvex optimal control and variational problems. It is a valuable addition to the control theory literature.” (Jafar Zafarani, zbMATH, Vol. 1270, 2013)