Overview
- Presents progress in the studies of nonconvex optimal control and variational problems
- Employs the Baire category approach to consider problems that do not satisfy convexity assumptions
- Establishes the well-posedness of a typical optimal control problem without convexity assumptions?
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 82)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
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.
Reviews
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)Authors and Affiliations
Bibliographic Information
Book Title: Nonconvex Optimal Control and Variational Problems
Authors: Alexander J. Zaslavski
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-1-4614-7378-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-7377-0Published: 11 June 2013
Softcover ISBN: 978-1-4899-9622-0Published: 06 July 2015
eBook ISBN: 978-1-4614-7378-7Published: 12 June 2013
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: XI, 378
Topics: Calculus of Variations and Optimal Control; Optimization, Optimization