Convex Analysis and Monotone Operator Theory in Hilbert Spaces by Heinz H. Bauschke

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

byHeinz H. Bauschke

Hardcover | May 3, 2011

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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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Title:Convex Analysis and Monotone Operator Theory in Hilbert SpacesFormat:HardcoverDimensions:484 pages, 9.25 × 6.1 × 0 inPublished:May 3, 2011Publisher:SpringerLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441994661

ISBN - 13:9781441994660

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Table of Contents

Background.- Hilbert Spaces.- Convex sets.- Convexity and Nonexpansiveness.- Fej´er 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.

Editorial 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)