Lecture Plan
The course (so far) can be summarised into the following list of topics, with the additional notes and materials:
| Topic | Material | N&W | Additional Notes |
|---|---|---|---|
| T0 - Introduction | Chapters 1&2 | Minimizers | |
| T1 - Convex functions and optimality conditions | N&W 2.1, additional notes on convexity and minimisers | Chapters 1&2 | Convex Functions |
| T2 - Line search methods | N&W 2.2(excluding trust-region content)-3.3 (up to Newton convergence) | Chapter 2.2, 3.1-3.3 | Convergence of backtracking |
| T3 - Conjugate gradient methods | N&W 5.1-5.2 | Chapter 5 | |
| T4 - Constrained optimisation | N&W 12.1-12.6 | Chapter 12 | Optimisation with convex constraints |
| T5 - Penalty and augmented Lagrangian methods | N&W 17 | Chapter 17 | |
| T6 - Trust-region methods | N&W 4.0, 4.3, 4.1 | Chapter 4 | |
| T7 - Quasi-Newton methods | N&W 6.1, 7.2, 6.2 | Chapter 6 | |
| T8 - More on constrained minimisation, and linear programming | See plan below | Chapter 12 + parts of 13 | All lecture notes (Mats) |
The lecture plan is as follows:
| Week | Taught by | Topic |
|---|---|---|
| 2 | - | No classes this week! |
| 3 (12/1) | Elisabeth | T0 |
| 4 (19/1) | - | No classes this week |
| 5 (26/1) | James | T1 |
| 6 (2/2) | James | T2 |
| 7 (9/2) | James | T2 & T3 |
| 8 (16/2) | James | T3 |
| 9 (23/2) | James | T4: Introduction, examples and motivation. |
| 10 (2/3) | Mats | T4: Repetition of 12.1–12.2. 12.3 KKT conditions, 12.4 proof of KKT theorem. 12.5 Definition of critical cone and Theorems 12.5–12.6 without proofs. 12.6 Linear constraint qualifications + MFCQ (just to be aware of other CQs; no proofs). Lecture notes |
| 11 (9/3) | James | T5 |
| 12 (16/3) | James | T6 |
| 13 (23/3) | James | T6 & T7 |
| 14 (30/3) | - | Easter Holidays - No teaching |
| 15 (6/4) | Mats | More on constrained minimisation: Chapter 12 up to and including 12.7 + some more geometry Tuesday. Planned: rest of Chapter 12 and a bit on linear programming Friday. |
| 16 (13/4) | Mats | Still progressing through Chapter 12. This week has rehearsed some on second-order conditions from 12.5, and introduced and proved duality propositions as in 12.9. We continue Friday with the examples on linear and quadratic programming from the same chapter, and then move on to the start of Chapter 13, with some more on the geometry of feasible sets for linear constraints. Lecture notes (for weeks 15 and 16) |
| 17 (20/4) | Mats | Linear programming and the simplex method. 13.0–13.3. Lecture notes |
| 18 (27/4) | James | Repetition and exam preparation |