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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bauschke, Heinz H. (Autor), Combettes, Patrick L. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2011.
Edición:1st ed. 2011.
Colección:CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
Temas:
Mathematical optimization.
Calculus of variations.
Algorithms.
Information visualization.
Calculus of Variations and Optimization.
Data and Information Visualization.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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