Convex Analysis and Monotone Operator Theory in Hilbert Spaces

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.

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)

• 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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