Authors:
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
Part of the book series: CMS Books in Mathematics (CMSBM)
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Table of contents (29 chapters)

Front Matter
About this book
This book presents a largely selfcontained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable.
Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book.
Author Information:
Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his "DiplomMathematiker (mit Auszeichnung)" from Goethe Universität in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. In 2009, he became UBCO's first "Researcher of the Year".
Patrick L. Combettes received the Brevet d'Études du Premier Cycle from Académie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Université Pierre et Marie Curie  Paris 6, laboratoire JacquesLouis Lions, where he is presently a Professeur de Classe Exceptionnelle.
He was elected Fellow of the IEEE in 2005.
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, wellwritten, informative and readable book is a largely selfcontained 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 JacquesLouis Lions, Université Pierre et Marie Curie, Paris, France
Patrick L. Combettes
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/10.1007/9781441994677
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Series ISSN: 16135237
Series EISSN: 21974152
Edition Number: 1
Number of Pages: XVI, 468
Topics: Calculus of Variations and Optimization, Algorithms, Data and Information Visualization