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Springer Optimization and Its Applications

Nonconvex Optimal Control and Variational Problems

Authors: Zaslavski, Alexander J.

  • ​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

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)

Table of contents (12 chapters)

  • Introduction

    Zaslavski, Alexander J.

    Pages 1-15

  • Well-posedness of Optimal Control Problems Without Convexity Assumptions

    Zaslavski, Alexander J.

    Pages 17-62

  • Well-posedness and Porosity in Nonconvex Optimal control

    Zaslavski, Alexander J.

    Pages 63-85

  • Well-posedness of Nonconvex Variational Problems

    Zaslavski, Alexander J.

    Pages 87-124

  • Generic Well-posedness Result for a Class of Optimal Control Problems

    Zaslavski, Alexander J.

    Pages 125-157

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-7378-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4614-7377-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4899-9622-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Nonconvex Optimal Control and Variational Problems
Authors
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