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CMS Books in Mathematics

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Authors: Bauschke, Heinz H., Combettes, Patrick L.

  • Tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness
  • Accessible to a broad audience
  • Coverage of many applications of interest to practitioners in finite- and infinite- dimensional spaces
  • More than 500 exercises are distributed throughout the book 
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Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-48311-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA in USD
  • ISBN 978-3-319-48310-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA in USD
  • ISBN 978-3-319-83911-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated.

Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada.

Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

About the authors

Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada.

Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

Table of contents (30 chapters)

  • Background

    Bauschke, Heinz H. (et al.)

    Pages 1-26

  • Hilbert Spaces

    Bauschke, Heinz H. (et al.)

    Pages 27-47

  • Convex Sets

    Bauschke, Heinz H. (et al.)

    Pages 49-68

  • Convexity and Notions of Nonexpansiveness

    Bauschke, Heinz H. (et al.)

    Pages 69-89

  • Fejér Monotonicity and Fixed Point Iterations

    Bauschke, Heinz H. (et al.)

    Pages 91-109

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-48311-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA in USD
  • ISBN 978-3-319-48310-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA in USD
  • ISBN 978-3-319-83911-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Authors
Series Title
CMS Books in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-48311-5
DOI
10.1007/978-3-319-48311-5
Hardcover ISBN
978-3-319-48310-8
Softcover ISBN
978-3-319-83911-0
Series ISSN
1613-5237
Edition Number
2
Number of Pages
XIX, 619
Number of Illustrations
18 b/w illustrations
Topics