Convex Analysis and Monotone Operator Theory in Hilbert Spaces (original) (raw)

Overview

Authors:

• Patrick L. Combettes 1

1. Heinz H. Bauschke
   1. Okanagan Campus, Department of Mathematics and Statistic, University of British Columbia, Kelowna, Canada
2. Patrick L. Combettes
   1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

• Tight interplay between 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

• Includes supplementary material: sn.pub/extras

• 320k Accesses

• 2538 Citations

• 12 Altmetric

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About this book

This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. A concise exposition of related constructive fixed point theory is presented, that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, best approximation theory, and convex feasibility. The book is accessible to a broad audience, and reaches out in particular to applied scientists and engineers, to whom these tools have become indispensable.

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Table of contents (29 chapters)

1. Background

   • Heinz H. Bauschke, Patrick L. Combettes
     Pages 1-25

2. Convex Sets

   • Heinz H. Bauschke, Patrick L. Combettes
     Pages 43-58

3. Conjugation

   • Heinz H. Bauschke, Patrick L. Combettes
     Pages 181-195

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Reviews

From the reviews:

“This book is devoted to a review of basic results and applications of convex analysis, monotone operator theory, and the theory of nonexpansive mappings in Hilbert spaces. … Each chapter concludes with an exercise section. Bibliographical pointers, a summary of symbols and notation, an index, and a comprehensive reference list are also included. The book is suitable for graduate students and researchers in pure and applied mathematics, engineering and economics.” (Sergiu Aizicovici, Zentralblatt MATH, Vol. 1218, 2011)

“This timely, well-written, informative and readable book is a largely self-contained exposition of the main results … in Hilbert spaces. … The high level of the presentation, the careful and detailed discussion of many applications and algorithms, and last, but not least, the inclusion of more than four hundred exercises, make the book accessible and of great value to students, practitioners and researchers … .” (Simeon Reich, Mathematical Reviews, Issue 2012 h)

Authors and Affiliations

• Okanagan Campus, Department of Mathematics and Statistic, University of British Columbia, Kelowna, Canada

Heinz H. Bauschke

• Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

Patrick L. Combettes

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Bibliographic Information

• Book Title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces
• Authors: Heinz H. Bauschke, Patrick L. Combettes
• Series Title: CMS Books in Mathematics
• DOI: https://doi.org/10.1007/978-1-4419-9467-7
• Publisher: Springer New York, NY
• eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
• Copyright Information: Springer Science+Business Media, LLC 2011
• eBook ISBN: 978-1-4419-9467-7Published: 19 April 2011
• Series ISSN: 1613-5237
• Series E-ISSN: 2197-4152
• Edition Number: 1
• Number of Pages: XVI, 468
• Topics: Calculus of Variations and Optimal Control; Optimization, Algorithms, Visualization

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