Convex Optimization - FRT015F
Graduate course (7.5 ECTS credits) given at the Department of Automatic Control, February to April, 2015. The course follows EE364a at Stanford closely.
First meeting Feb 10 2015, 15.15-17.00 in Konferensrum 1167B in the lab corridor of the Department of Automatic Control.
General Information
Organizer: Pontus Giselsson send me an email to be added to the course email list.
Meetings: Tuesdays 15.15-17.00, see schedule below. These will be exercise sessions.
Lectures: Online video lectures by Stephen Boyd are available here. The participants should view roughly two of these video lectures per week. There will be no separate lectures held in Lund, we will focus entirely on exercise sessions.
Textbook
The textbook by Stephen Boyd and Lieven Vandenberghe is published by Cambridge University Press, who also makes it freely available for download.
Lectures and Reading
Read and watch the following material before solving the exercises that are due on the listed date.
- 17 feb (video lectures 1-2, book chapters 1-2, slides: 1.1-2.23): Introduction. Convex sets.
- 24 feb (video lectures 3-4, book chapters 3-4.1, slides: 3.1-4.3): Convex functions. Convex optimization problems.
- 3 mars (video lectures 5-7, book chapter 4, slides: 4.1-4.47): Convex optimization problems.
- 10 mars (video lectures 8-9, book chapter 5, slides: 5.1-5.30): Duality.
- 17 mars (video lectures 10-11, book chapters 6-7, slides: 6.1-7.15): Approximation and fitting. Statistical estimation.
- 24 mars (video lectures 12-13, book chapters 7-8, slides: 7.1-8.16): Statistical estimation. Geometric problems.
- 31 mars (video lectures 14-16, book chapters 9, Appendix C, slides: 9.1-10.30): Numerical linear algebra. Unconstrained minimization.
- 10 april, 13-15 (slides): Additional lecture on monotone operators and fixed-point iterations (optional).
- 14 april (video lectures 17-19, book chapters 10-11, slides: 11.1-13.6): Equality constrained minimization. Interior-point methods.
Exercises and Handins
Before exercise sessions, fill in this exercise_list.
Exercise schedule: At meetings, the participants should show and discuss solutions to the exercises. The handins, in bold face below, should be done individually and handed in before the exercise session. The handin grading will be based on the best 7 of your handins.
- 17 feb: 2.6, 2.9, 2.12a-e, 2.15, 2.24a, 2.25, 2.28.
- 24 feb: 3.2, 3.16, 3.24a-f, 4.1, A1.7, A2.1, A2.2, A3.2.
- 3 mars: 3.36(a,d), 3.42, 3.49a-c, 4.8a-e, 4.15, 4.17, A3.4, A13.3.
- 10 mars: 5.1, 5.13, A2.27, A3.18, A3.26, A4.1.
- 17 mars: 5.5, 6.2, 7.6, A5.12, A13.4, A13.9, A16.9.
- 24 mars: 8.16, A6.6, A6.13, A13.12, A14.8.
- 31 mars: 9.30 + A8.3, A3.20, A5.15, A13.14, and A17.3.
- 14 april: A3.31, A9.5, A16.1, and A17.1.
All numbered exercises are from the textbook; exercises which start with ‘A’ are from the set of additional exercises posted on the textbook website. Data files for the additional exercises can be found on the textbook page.
Software
- Matlab optimization modeling CVX
- Python optimization modeling CVXPY
- Julia optimization modeling Convex.jl
You should make sure to have installed and can use CVX, CVXPY, or Convex.jl.
Examination
The examination will be based on weekly home problems (14p) and a take-home exam (21p). The limit for pass is 18p out of 35p. The 24 hour take-home exam is scheduled to take place the 29th of April. I will, via email, send the exam to the course participants at 09:00 on the 29th.
Project (+2.5hp)
It is possible to add a project to the course. Projects can be done in groups of 1-3 persons. I would encourage you to find your own project formulations, perhaps with relation to your own research. Projects could range from numerical experiments to purely mathematical projects. There are three mandatory parts of the project:
- Project description (some sentences are enough), deadline: April 3.
- Project report (small, informal), deadline: TBD
- Project presentation (10 min): TBD