Convex Analysis and Monotone Operator Theory in Hilbert Spaces

1. Background
Heinz H. Bauschke, Patrick L. Combettes

2. Hilbert Spaces
Heinz H. Bauschke, Patrick L. Combettes

3. Convex Sets
Heinz H. Bauschke, Patrick L. Combettes

4. Convexity and Nonexpansiveness
Heinz H. Bauschke, Patrick L. Combettes

5. Fejér Monotonicity and Fixed Point Iterations
Heinz H. Bauschke, Patrick L. Combettes

6. Convex Cones and Generalized Interiors
Heinz H. Bauschke, Patrick L. Combettes

7. Support Functions and Polar Sets
Heinz H. Bauschke, Patrick L. Combettes

8. Convex Functions
Heinz H. Bauschke, Patrick L. Combettes

9. Lower Semicontinuous Convex Functions
Heinz H. Bauschke, Patrick L. Combettes

10. Convex Functions: Variants
Heinz H. Bauschke, Patrick L. Combettes

11. Convex Variational Problems
Heinz H. Bauschke, Patrick L. Combettes

12. Infimal Convolution
Heinz H. Bauschke, Patrick L. Combettes

13. Conjugation
Heinz H. Bauschke, Patrick L. Combettes

14. Further Conjugation Results
Heinz H. Bauschke, Patrick L. Combettes

15. Fenchel–Rockafellar Duality
Heinz H. Bauschke, Patrick L. Combettes

16. Subdifferentiability
Heinz H. Bauschke, Patrick L. Combettes

17. Differentiability of Convex Functions
Heinz H. Bauschke, Patrick L. Combettes

18. Further Differentiability Results
Heinz H. Bauschke, Patrick L. Combettes

19. Duality in Convex Optimization
Heinz H. Bauschke, Patrick L. Combettes

20. Monotone Operators
Heinz H. Bauschke, Patrick L. Combettes

21. Finer Properties of Monotone Operators
Heinz H. Bauschke, Patrick L. Combettes

22. Stronger Notions of Monotonicity
Heinz H. Bauschke, Patrick L. Combettes

23. Resolvents of Monotone Operators
Heinz H. Bauschke, Patrick L. Combettes

24. Sums of Monotone Operators
Heinz H. Bauschke, Patrick L. Combettes

25. Zeros of Sums of Monotone Operators
Heinz H. Bauschke, Patrick L. Combettes

26. Fermat’s Rule in Convex Optimization
Heinz H. Bauschke, Patrick L. Combettes

27. Proximal Minimization
Heinz H. Bauschke, Patrick L. Combettes

28. Projection Operators
Heinz H. Bauschke, Patrick L. Combettes

29. Best Approximation Algorithms
Heinz H. Bauschke, Patrick L. Combettes

Nyckelord: Mathematics, Calculus of Variations and Optimal Control, Optimization, Algorithms, Visualization