Convex Analysis and Monotone Operator Theory in Hilbert Spaces - Tapa blanda

Sinopsis

 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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