Convex analysis and monotone operator theory in hilbert spaces / Heinz H. Bauschke, Patrick L. Combettes.
Bauschke, Heinz H.; Combettes, Patrick L.
2011
QA322.4 .B38 2011
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Title Convex analysis and monotone operator theory in hilbert spaces / Heinz H. Bauschke, Patrick L. Combettes.
Author Bauschke, Heinz H.
ISBN 9781441994677 (electronic bk.)
144199467X (electronic bk.)
9781441994660
1441994661
3319483110
9783319483115
1461428696
1441994688
3319483102
DOI https://doi.org/10.1007/978-1-4419-9467-7
Publication Details New York : Springer, ©2011.
Language English
Language Note English.
Description 1 online resource (xvi, 468 pages)
Item Number 10.1007/978-1-4419-9467-7 doi
Call Number QA322.4 .B38 2011
Dewey Decimal Classification 515/.733
Summary This book presents a largely self-contained 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 "Diplom-Mathematiker (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 Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Description based on print version record.
Added Author Combettes, Patrick L.
Series CMS books in mathematics.
Available in Other Form Convex analysis and monotone operator theory in hilbert spaces.
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Background
Hilbert Spaces
Convex sets
Convexity and Nonexpansiveness
Fejér Monotonicity and Fixed Point Iterations
Convex Cones and Generalized Interiors
Support Functions and Polar Sets
Convex Functions
Lower Semicontinuous Convex Functions
Convex Functions: Variants
Convex Variational Problems
Infimal Convolution
Conjugation
Further Conjugation Results
Fenchel-Rockafellar Duality
Subdifferentiability
Differentiability of Convex Functions
Further Differentiability Results
Duality in Convex Optimization
Monotone Operators
Finer Properties of Monotone Operators
Stronger Notions of Monotonicity
Resolvents of Monotone Operators
Sums of Monotone Operators.-Zeros of Sums of Monotone Operators
Fermat's Rule in Convex Optimization
Proximal Minimization Projection Operators
Best Approximation Algorithms
Bibliographical Pointers
Symbols and Notation
References.

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