Convex Analysis and Monotone Operator Theory in Hilbert Spaces

515.64

Bauschke, Heinz H. Convex Analysis and Monotone Operator Theory in Hilbert Spaces by Heinz H. Bauschke, Patrick L. Combettes. - 2nd ed. 2017.. -
XIX, 619 p. 18 illus. online resource. - (CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ) Content notes : 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. 9783319483115 * Mathematical optimization. Algorithms. Visualization. Calculus of Variations and Optimal Control; Optimization. Algorithms. Visualization. * Combettes, Patrick L., aut, http://id.loc.gov/vocabulary/relators/aut * Title * Series