Heinz H. Bauschke, Patrick L. Combettes

Convex Analysis and Monotone Operator Theory in Hilbert Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer US
• Seitenzahl: 468
• Erscheinungstermin: 19. April 2011
• Englisch
• ISBN-13: 9781441994677
• Artikelnr.: 37351604

Autorenporträt

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.

Inhaltsangabe

Background.- Hilbert Spaces.- Convex Sets.- Convexity and Notation of Nonexpansiveness.- Fejer 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 Minimization Problems.- Infimal Convolution.- Conjugation.- Further Conjugation Results.- Fenchel-Rockafellar Duality.- Subdifferentiability of Convex Functions.- 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.- Proximity Operators.- Sums of Monotone Operators.- Zeros of Sums of Monotone Operators.- Fermat's Rule in Convex Optimization.- Proximal Minimization.- Projection Operators.- Best Approximation Algorithms.