Calculus Without Derivatives

  • Jean-Paul Penot
Part of the Graduate Texts in Mathematics book series (GTM, volume 266)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Jean-Paul Penot
    Pages 1-115
  3. Jean-Paul Penot
    Pages 117-186
  4. Jean-Paul Penot
    Pages 187-261
  5. Jean-Paul Penot
    Pages 263-356
  6. Jean-Paul Penot
    Pages 357-405
  7. Jean-Paul Penot
    Pages 407-462
  8. Jean-Paul Penot
    Pages 463-478
  9. Back Matter
    Pages 479-524

About this book

Introduction

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems.  Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. 

In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed.  The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

Keywords

Clarke subdifferential Newton Method approximation calculus of variations coderivative convex analysis differential calculus duality elementary subdifferentials error bounds fuzzy calculus limiting subdifferential mathematical programming nonsmooth analysis normal cone optimization stability theory tangent cone

Authors and affiliations

  • Jean-Paul Penot
    • 1
  1. 1.Laboratory of Applied MathematicsUniversité de Pau et des Pays de l'Adour Bâtiment IPRAPAU CEDEXFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4538-8
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4537-1
  • Online ISBN 978-1-4614-4538-8
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • About this book