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Convex Analysis and Monotone Operator Theory in Hilbert Spaces

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Cover of 'Convex Analysis and Monotone Operator Theory in Hilbert Spaces'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Background
  3. Altmetric Badge
    Chapter 2 Hilbert Spaces
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    Chapter 3 Convex Sets
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    Chapter 4 Convexity and Notions of Nonexpansiveness
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    Chapter 5 Fejér Monotonicity and Fixed Point Iterations
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    Chapter 6 Convex Cones and Generalized Interiors
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    Chapter 7 Support Functions and Polar Sets
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    Chapter 8 Convex Functions
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    Chapter 9 Lower Semicontinuous Convex Functions
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    Chapter 10 Convex Functions: Variants
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    Chapter 11 Convex Minimization Problems
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    Chapter 12 Infimal Convolution
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    Chapter 13 Conjugation
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    Chapter 14 Further Conjugation Results
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    Chapter 15 Fenchel–Rockafellar Duality
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    Chapter 16 Subdifferentiability of Convex Functions
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    Chapter 17 Differentiability of Convex Functions
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    Chapter 18 Further Differentiability Results
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    Chapter 19 Duality in Convex Optimization
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    Chapter 20 Monotone Operators
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    Chapter 21 Finer Properties of Monotone Operators
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    Chapter 22 Stronger Notions of Monotonicity
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    Chapter 23 Resolvents of Monotone Operators
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    Chapter 24 Proximity Operators
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    Chapter 25 Sums of Monotone Operators
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    Chapter 26 Zeros of Sums of Monotone Operators
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    Chapter 27 Fermat’s Rule in Convex Optimization
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    Chapter 28 Proximal Minimization
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    Chapter 29 Projection Operators
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    Chapter 30 Best Approximation Algorithms
Attention for Chapter 19: Duality in Convex Optimization
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Chapter title
Duality in Convex Optimization
Chapter number 19
Book title
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Published by
Springer, Cham, January 2017
DOI 10.1007/978-3-319-48311-5_19
Book ISBNs
978-3-31-948310-8, 978-3-31-948311-5
Authors

Heinz H. Bauschke, Patrick L. Combettes