Convex Analysis and Monotone Operator Theory in Hilbert Spaces

• Main Authors: Bauschke, Heinz H. (Author), Combettes, Patrick L. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
• Subjects: Mathematics.; Algorithms.; Visualization.; Calculus of variations.; Calculus of Variations and Optimal Control; Optimization.

This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the...

Table of Contents:

• 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.