Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: CMS Books in Mathematics (CMSBM)
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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 Mathematicsin 2016.
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Keywords
Table of contents (31 chapters)
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Front Matter
Authors and Affiliations
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.
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/10.1007/978-3-319-48311-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-48310-8Published: 08 March 2017
Softcover ISBN: 978-3-319-83911-0Published: 03 May 2018
eBook ISBN: 978-3-319-48311-5Published: 28 February 2017
Series ISSN: 1613-5237
Series E-ISSN: 2197-4152
Edition Number: 2
Number of Pages: XIX, 619
Number of Illustrations: 18 b/w illustrations
Topics: Calculus of Variations and Optimal Control; Optimization, Algorithms, Visualization