Convex Analysis and Monotone Operator Theory in Hilbert Spaces

  • Heinz H. Bauschke
  • Patrick L. Combettes

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Heinz H. Bauschke, Patrick L. Combettes
    Pages 1-26
  3. Heinz H. Bauschke, Patrick L. Combettes
    Pages 27-47
  4. Heinz H. Bauschke, Patrick L. Combettes
    Pages 49-68
  5. Heinz H. Bauschke, Patrick L. Combettes
    Pages 69-89
  6. Heinz H. Bauschke, Patrick L. Combettes
    Pages 91-109
  7. Heinz H. Bauschke, Patrick L. Combettes
    Pages 111-132
  8. Heinz H. Bauschke, Patrick L. Combettes
    Pages 133-138
  9. Heinz H. Bauschke, Patrick L. Combettes
    Pages 139-156
  10. Heinz H. Bauschke, Patrick L. Combettes
    Pages 157-176
  11. Heinz H. Bauschke, Patrick L. Combettes
    Pages 177-187
  12. Heinz H. Bauschke, Patrick L. Combettes
    Pages 189-201
  13. Heinz H. Bauschke, Patrick L. Combettes
    Pages 203-217
  14. Heinz H. Bauschke, Patrick L. Combettes
    Pages 219-236
  15. Heinz H. Bauschke, Patrick L. Combettes
    Pages 237-246
  16. Heinz H. Bauschke, Patrick L. Combettes
    Pages 247-262
  17. Heinz H. Bauschke, Patrick L. Combettes
    Pages 263-287
  18. Heinz H. Bauschke, Patrick L. Combettes
    Pages 289-312
  19. Heinz H. Bauschke, Patrick L. Combettes
    Pages 313-327
  20. Heinz H. Bauschke, Patrick L. Combettes
    Pages 329-347

About this book

Introduction

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.

Keywords

Convex analysis monotone operator nonexpansive operator proximal algorithm fixed point algorithm operator splitting algorithm convex optimization

Authors and affiliations

  • Heinz H. Bauschke
    • 1
  • Patrick L. Combettes
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaKelownaCanada
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-48311-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-48310-8
  • Online ISBN 978-3-319-48311-5
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • About this book