Nonconvex Optimal Control and Variational Problems
Authors: Zaslavski, Alexander J.
Free Preview- 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
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- About this book
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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
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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)
- Table of contents (12 chapters)
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Introduction
Pages 1-15
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Well-posedness of Optimal Control Problems Without Convexity Assumptions
Pages 17-62
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Well-posedness and Porosity in Nonconvex Optimal control
Pages 63-85
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Well-posedness of Nonconvex Variational Problems
Pages 87-124
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Generic Well-posedness Result for a Class of Optimal Control Problems
Pages 125-157
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Table of contents (12 chapters)
- Download Preface 1 PDF (168.7 KB)
- Download Sample pages 1 PDF (449.4 KB)
- Download Table of contents PDF (2.1 MB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Nonconvex Optimal Control and Variational Problems
- Authors
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- Alexander J. Zaslavski
- Series Title
- Springer Optimization and Its Applications
- Series Volume
- 82
- Copyright
- 2013
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4614-7378-7
- DOI
- 10.1007/978-1-4614-7378-7
- Hardcover ISBN
- 978-1-4614-7377-0
- Softcover ISBN
- 978-1-4899-9622-0
- Series ISSN
- 1931-6828
- Edition Number
- 1
- Number of Pages
- XI, 378
- Topics
