Shuvomoy Das Gupta

These are my handwritten notes on monotone operator theory and operator splitting based on Convex Analysis and Monotone Operator Theory in Hilbert Spaces by Bauschke and Combettes

• Chapter 1. Background

• Chapter 2. Hilbert Spaces

• Chapter 3. Convex Sets

• Chapter 4. Convexity and nonexpansiveness

• Chapter 5. Fejer Monotonicity and Fixed Point

• Chapter 6. Convex Cones and Generalized Interiors

• Chapter 7. Support Functions and Polar Sets

• Chapter 8. Convex Functions

• Chapter 9. Lower Semicontinuous Convex Functions

• Chapter 10. Convex Functions Variants

• Chapter 11. Convex Variational Problems

• Chapter 12. Infimal Convolution

• Chapter 13. Conjugation

• Chapter 14. Further Conjugation Results

• Chapter 15. Fenchel-Rockafellar Duality

• Chapter 16. Subdifferentiality

• Chapter 17. Gateaux and Frechet Differentiability

• Chapter 18. Further Differentiability Results

• Chapter 19. Duality in Convex Optimization

• Chapter 20. Monotone Operators

• Chapter 21. Finer Properties of Monotone Operator

• Chapter 23. Resolvents of Monotone Operators

• Chapter 24. Sums of Monotone Operators

• Chapter 25. Zeros of Sums of Monotone Operators

• Chapter 26. Fermat's Rule in Convex Optimization

• Chapter 27. Proximal Minimization

• Chapter 28. Projection Operators

• Chapter 29. Best Approximation Algorithms

These notes are based on the course EE364b

• 0. Notation

• 1. Subgradient

• 2. Subgradient calculus

• 3. Subgradient methods

• 4. Subgradient methods for constrained optimization problems

• 5. Primal-dual subgradient method

• 6. Introduction to proximal mapping

• 7. Proximal algorithm

• 8. Proximal gradient algorithm

• 9. Projections onto different sets

• 10. Computing proximal maps and projections

• 11. Parallel and distributed algorithms

• 12. Coordinate descent algorithm

• 13. Revisiting decomposition algorithms

• 14. Distributed optimization algorithm by circuits

• 15. Introduction to monotone operators

• 16. Nonexpansive and contraction mapping

• 17. Resolvent and Cayley operator

• 18. Fixed point iteration

• 19. Proximal point algorithm and method of multipliers

• 20. Davis-Yin Operator Splitting

• 21. Operator splitting algorithms, Douglas-Rachford splitting

• 22. Consensus optimization

• 23. ADMM from operator splitting

• 24. ADMM classical derivation