Convex Analysis and Monotone Operator Theory in Hilbert Spaces
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...
Κύριοι συγγραφείς: | , |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2017.
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Έκδοση: | 2nd ed. 2017. |
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 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.