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...
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| Glavni autori: | , |
|---|---|
| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
New York, NY :
Springer New York
2011.
Cham : Springer Nature |
| Serija: | CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
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| Teme: | |
| Online pristup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Bilješka: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Texte imprimé, 9781441994684 • Convex analysis and monotone operator theory in Hilbert spaces, Heinz H. Bauschke, Patrick L. Combettes, 2011, New York, Springer, 1 volume (XVI-468 pages), CMS Books in mathematics, 978-1-4419-9466-0 • Convex analysis and monotone operator theory in Hilbert spaces, Heinz H. Bauschke, Patrick L. Combettes, 2011, New York, Springer, 1 volume (XVI-468 pages), CMS Books in mathematics, 978-1-4419-9466-0 |
Sadržaj:
- 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.