Functional Analysis, Calculus of Variations and Optimal Control

  • Francis Clarke

Part of the Graduate Texts in Mathematics book series (GTM, volume 264)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Functional Analysis

    1. Front Matter
      Pages 1-1
    2. Francis Clarke
      Pages 3-25
    3. Francis Clarke
      Pages 27-46
    4. Francis Clarke
      Pages 47-58
    5. Francis Clarke
      Pages 59-74
    6. Francis Clarke
      Pages 75-103
    7. Francis Clarke
      Pages 105-131
    8. Francis Clarke
      Pages 133-155
    9. Francis Clarke
      Pages 157-169
  3. Optimization and Nonsmooth Analysis

    1. Front Matter
      Pages 171-171
    2. Francis Clarke
      Pages 173-191
    3. Francis Clarke
      Pages 193-225
    4. Francis Clarke
      Pages 227-254
    5. Francis Clarke
      Pages 255-272
    6. Francis Clarke
      Pages 273-283
  4. Calculus of Variations

    1. Front Matter
      Pages 285-285
    2. Francis Clarke
      Pages 287-305
    3. Francis Clarke
      Pages 307-318
    4. Francis Clarke
      Pages 319-334

About this book


Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor.

This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods.

The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering.

Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.


Calculus of Variations Continuous Optimization Dynamic Optimization Functional Analysis Optimal Control

Authors and affiliations

  • Francis Clarke
    • 1
  1. 1.Institut Camille JordanUniversité Claude Bernard Lyon 1 Institut Camille JordanVilleurbanneFrance

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-4819-7
  • Online ISBN 978-1-4471-4820-3
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • About this book
Industry Sectors