Convex Analysis and Monotone Operator Theory in Hilbert Spaces
This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay...
| Κύριοι συγγραφείς: | , |
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| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
New York, NY :
Springer New York,
2011.
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| Σειρά: | CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
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| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.
