Convex analysis and monotone operator theory in Hilbert spaces

    • Bauschke, Heinz H.
    • Combettes, Patrick L.

Author(s)

    • Bauschke, Heinz H.
    • Combettes, Patrick L.

Bibliographic Information

Convex analysis and monotone operator theory in Hilbert spaces

Heinz H. Bauschke, Patrick L. Combettes

(CMS books in mathematics)

Springer, c2011

Available at  / 25 libraries

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Note

Includes bibliographical references and index

Description and Table of Contents

Description

This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. A concise exposition of related constructive fixed point theory is presented, that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, best approximation theory, and convex feasibility. The book is accessible to a broad audience, and reaches out in particular to applied scientists and engineers, to whom these tools have become indispensable.

Table of Contents

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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Details

  • NCID
    BB05814531
  • ISBN
    • 9781441994660
  • LCCN
    2011926587
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    New York, NY
  • Pages/Volumes
    xvi, 468 p.
  • Size
    25 cm
  • Parent Bibliography ID
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