Grundlehren Text Editions

Fundamentals of Convex Analysis

Authors: Hiriart-Urruty, Jean-Baptiste, Lemaréchal, Claude

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  • ISBN 978-3-642-56468-0
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  • ISBN 978-3-540-42205-1
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About this Textbook

This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published - by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. Now [18] hasa dual but clearly defined nature: - an introduction to the basic concepts in convex analysis, - a study of convex minimization problems (with an emphasis on numerical al- rithms), and insists on their mutual interpenetration. It is our feeling that the above basic introduction is much needed in the scientific community. This is the motivation for the present edition, our intention being to create a tool useful to teach convex anal­ ysis. We have thus extracted from [18] its "backbone" devoted to convex analysis, namely ChapsIII-VI and X. Apart from some local improvements, the present text is mostly a copy of the corresponding chapters. The main difference is that we have deleted material deemed too advanced for an introduction, or too closely attached to numerical algorithms. Further, we have included exercises, whose degree of difficulty is suggested by 0, I or 2 stars *. Finally, the index has been considerably enriched. Just as in [18], each chapter is presented as a "lesson", in the sense of our old masters, treating of a given subject in its entirety.

Reviews

From the reviews of the first edition:

"...This book is an abridged version of the book "Convex Analysis and Minimization Algorithms" (shortly CAMA) written in two volumes by the same authors... . The authors have extracted from CAMA Chapters III-VI and X, containing the fundamentals of convex analysis, deleting material seemed too advanced for an introduction, or too closely attached to numerical algorithms. Each Chapter is presented as a "lesson" treating a given subject in its entirety, completed by numerous examples and figures. So, this new version becomes a good book for learning and teaching of convex analysis in finite dimensions...."

S. Mititelu in "Zentralblatt für Mathematik und ihre Grenzgebiete", 2002

"I believe that the book under review will become the standard text doing much to implement the type of course Victor Klee was advocating and covering as it does the considerable recent development of the subject. … If you are looking for a well-designed text for a course on convex analysis, preliminary to one on optimization or nonlinear analysis then this is the one which will certainly be a standard for many years." (John Giles, The Australian Mathematical Society Gazette, Vol. 29 (2), 2002)


Table of contents (6 chapters)

  • Introduction: Notation, Elementary Results

    Hiriart-Urruty, Jean-Baptiste (et al.)

    Pages 1-17

  • Convex Sets

    Hiriart-Urruty, Jean-Baptiste (et al.)

    Pages 19-72

  • Convex Functions

    Hiriart-Urruty, Jean-Baptiste (et al.)

    Pages 73-120

  • Sublinearity and Support Functions

    Hiriart-Urruty, Jean-Baptiste (et al.)

    Pages 121-162

  • Subdifferentials of Finite Convex Functions

    Hiriart-Urruty, Jean-Baptiste (et al.)

    Pages 163-208

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-56468-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-42205-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fundamentals of Convex Analysis
Authors
Series Title
Grundlehren Text Editions
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-56468-0
DOI
10.1007/978-3-642-56468-0
Softcover ISBN
978-3-540-42205-1
Edition Number
1
Number of Pages
X, 259
Additional Information
Based on volume 305 and 306 in the series: Grundlehren der mathematischen Wissenschaften, 1993
Topics