Topics in Convex Optimisation (Lent 2022)

1. Lecture 1: Introduction
2. Lecture 2: Review of convexity
3. Lecture 3: Gradient method
4. Lecture 4: Fast gradient method
5. Lecture 5: Subgradients
6. Lecture 6: Subgradient method
7. Lecture 7: Constrained optimization and duality
8. Lecture 8: Duality (continued) and KKT conditions
9. Lecture 9: Projections and projected (sub)gradient methods
10. Lecture 10: Proximal methods
11. Lecture 11: Bregman proximal methods
12. Lecture 12: Dual methods
13. Lecture 13: Augmented Lagrangian, ADMM
14. Lecture 14: Douglas-Rachford
15. Lecture 15: Newton's method
16. Lecture 15: Newton's method (continued)

Exercise sheets

• Exercise sheet 1 - Example class Wed Feb 9th, 2-3.30pm, MR4
• Exercise sheet 2 - Example class Wed Mar 2nd, 2-3.30pm, MR4
• Exercise sheet 3 - Example class Wed Mar 16th, 2-3.30pm, MR4

References

• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press.
• Yurii Nesterov, Introductory Lectures on Convex Optimization, Springer.
• Lieven Vandenberghe, Lecture slides for EE236C at UCLA.
• Sébastien Bubeck, Convex Optimization: Algorithms and Complexity
• G. Gordon and R. Tibshirani, Lecture notes for an optimization course at CMU
• N. Parikh and S. Boyd, Proximal algorithms. [A monograph about proximal operators and algorithms]
• S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers . [A monograph about ADMM and its applications in distributed optimization and statistical learning]
• J. Renegar, A Mathematical View of Interior Point Methods for Convex Optimization. [A monograph about path-following interior-point methods using self-concordant functions]
• R.T. Rockafellar, Convex Analysis, Princeton Mathematical Series