Topics in Convex Optimisation (Lent 2023)

1. Lecture 1: Introduction
2. Lecture 2: Review of convexity
3. Lecture 3: Smoothness and strong-convexity
4. Lecture 4: Gradient method
5. Lecture 5: Fast gradient method
6. Lecture 6: Lower complexity bounds
7. Lecture 7: Subgradients
8. Lecture 8: Subgradient method
9. Lecture 9: Proximal mapping
10. Lecture 10: Proximal gradient methods
11. Lecture 11: Bregman gradient methods / mirror descent
12. Lecture 12: Conjugate functions / Lagrange duality
13. Lecture 13: Dual methods
14. Lecture 14: ADMM / Douglas-Rachford
15. Lecture 15: Newton's method
16. Lecture 16: Newton's method (continued)

Exercise sheets

• Exercise sheet 1 - Example class Thu Feb 9th, 3.30-5pm, MR11
• Exercise sheet 2 - Example class Thu Feb 23rd, 3.30-5pm, MR11
• Exercise sheet 3 - Example class Thu Mar 9th, 3.30-5pm, MR11

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