The main theme is to teach convex analysis for signal processing and machine learning. I will follow basically the stanford lecture note EE 236C. I will cover:
1. Convex function and gradient method
2. Convergence rate and strongly convex function
3. Conjugate function and subgradient
4. Directional derivation, subgradient calculation and method
5. Proximal point method and proximal gradient method for sparse inverse problems
6. Constrained optimization (Convex optimization book) and Lagrangian method
7. Penalty method and augmented Lagrangian method
8. Alternating direction method of multipliers
9. Variational inequality, block coordinate descent.
10. Smooth and Moreau envelope
11. Concensus and SVM and Acceleration