Topics in Convex Optimisation (Michaelmas 2019)

1. Lecture 1: Introduction
2. Lecture 2: Review of convex functions
3. Lecture 3: Gradient method
4. Lecture 4: Lower complexity bounds
5. Lecture 5: Fast gradient method
6. Lecture 6: Proximal gradient method
7. Lecture 7: Subgradient method
8. Lecture 8: Conjugate functions
9. Lecture 9: Smoothing
10. Lecture 10: Lagrangian duality
11. Lecture 11: Dual methods
12. Lecture 12: Mirror descent
13. Lecture 13: Newton's method
14. Lecture 14: Self-concordant functions
15. Lecture 15: Path-following methods
16. Lecture 16: Linear/second-order cone/semidefinite programming

Note on subdifferential of sum of two convex functions.

Exercise sheets

1. Exercise sheet 1. To be discussed at the first example class, Tuesday 5th November 3:30pm, MR9. Solutions
2. Exercise sheet 2. To be discussed at the second example class, Tuesday 19th November 3:30pm, MR9. Solutions
3. Exercise sheet 3. To be discussed at the third example class, Tuesday 3rd December 3:30pm, MR9. Solutions

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]
• J. Renegar, A Mathematical View of Interior Point Methods for Convex Optimization. [A monograph about path-following interior-point methods using self-concordant functions]