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Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Autorzy
Wydawnictwo Springer, Berlin
Data wydania
Liczba stron 468
Forma publikacji książka w miękkiej oprawie
Język angielski
ISBN 9781461428695
Kategorie Matematyka
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Opis książki

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.

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Spis treści

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.

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