Convexity and Optimization in Banach Spaces

  • Viorel Barbu
  • Teodor Precupanu

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Viorel Barbu, Teodor Precupanu
    Pages 1-65
  3. Viorel Barbu, Teodor Precupanu
    Pages 67-151
  4. Viorel Barbu, Teodor Precupanu
    Pages 153-232
  5. Viorel Barbu, Teodor Precupanu
    Pages 233-364
  6. Back Matter
    Pages 365-368

About this book


An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application.

This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems.

Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.


banach spaces convex function convex set duality theory optimal control problem subdifferential

Authors and affiliations

  • Viorel Barbu
    • 1
  • Teodor Precupanu
    • 2
  1. 1.Department of MathematicsUniversity Al. I. CuzaIasiRomania
  2. 2.Department of MathematicsUniversity Al. I. CuzaIasiRomania

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2012
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-007-2246-0
  • Online ISBN 978-94-007-2247-7
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site
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