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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Bauschke, Heinz H. (Συγγραφέας), Combettes, Patrick L. (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
Έκδοση:2nd ed. 2017.
Σειρά:CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
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.