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Über dieses Buch

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 ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated.

Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada.

Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

Inhaltsverzeichnis

Frontmatter

2017 | OriginalPaper | Buchkapitel

Chapter 1. Background

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 2. Hilbert Spaces

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 3. Convex Sets

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 4. Convexity and Notions of Nonexpansiveness

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 5. Fejér Monotonicity and Fixed Point Iterations

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 6. Convex Cones and Generalized Interiors

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 7. Support Functions and Polar Sets

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 8. Convex Functions

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 9. Lower Semicontinuous Convex Functions

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 10. Convex Functions: Variants

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 11. Convex Minimization Problems

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 12. Infimal Convolution

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 13. Conjugation

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 14. Further Conjugation Results

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 15. Fenchel–Rockafellar Duality

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 16. Subdifferentiability of Convex Functions

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 17. Differentiability of Convex Functions

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 18. Further Differentiability Results

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 19. Duality in Convex Optimization

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 20. Monotone Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 21. Finer Properties of Monotone Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 22. Stronger Notions of Monotonicity

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 23. Resolvents of Monotone Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 24. Proximity Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 25. Sums of Monotone Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 26. Zeros of Sums of Monotone Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 27. Fermat’s Rule in Convex Optimization

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 28. Proximal Minimization

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 29. Projection Operators

Heinz H. Bauschke, Patrick L. Combettes

2017 | OriginalPaper | Buchkapitel

Chapter 30. Best Approximation Algorithms

Heinz H. Bauschke, Patrick L. Combettes

Backmatter

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