# Convex Optimization 2018

Graduate course (7.5 ECTS credits) given at the Department of Automatic Control, November 2018-February 2019. The course follows EE364a at Stanford closely.

**The upcoming exercise sessions (except one) will take place in 2112 - "Seminarierummet" at Automatic Control. The exception is on Dec 13th when we will be in M:P1.**

#### General Information

Organizer: Pontus Giselsson, send an email to be added to the course email list.

Meetings: Thursdays 10.15-12.00, 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.

- 29 nov (video lectures 1-2, book chapters 1-2, slides: 1.1-2.23): Introduction. Convex sets.
- 6 dec (video lectures 3-4, book chapters 3-4.1, slides: 3.1-4.3): Convex functions. Convex optimization problems.
- 13 dec (video lectures 5-7, book chapter 4, slides: 4.1-4.47): Convex optimization problems.
- 20 dec (video lectures 8-9, book chapter 5, slides: 5.1-5.30): Duality.
- 10 jan (video lectures 10-11, book chapters 6-7, slides: 6.1-7.15): Approximation and fitting. Statistical estimation.
- 17 jan (video lectures 12-13, book chapters 7-8, slides: 7.1-8.16): Statistical estimation. Geometric problems.
- 24 jan (video lectures 14-16, book chapters 9, Appendix C, slides: 9.1-10.30): Numerical linear algebra. Unconstrained minimization.
- 31 jan (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.

- 29 nov: 2.6, 2.9, 2.12a-e, 2.15, 2.24a, 2.25, 2.28.
- 6 dec: 3.2, 3.16, 3.24a-f, 4.1, A1.7, A2.1, A2.2, A3.2.
- 13 dec: 3.36(a,d), 3.42, 3.49a-c, 4.8a-e, 4.15, 4.17, A3.4, A13.3.
- 20 dec: 5.1, 5.13, A2.27, A3.18, A3.26, A4.1.
- 10 jan: 5.5, 6.2, 7.6, A5.12, A13.4, A13.9, A16.9.
- 17 jan: 8.16, A6.6, A6.13, A13.12, A14.8.
- 24 jan: 9.30 + A8.3(A8.3), A3.20(A3.20), A5.15(A5.15), A13.14(A14.14), and A17.3(A18.3).
- 31 jan: A3.31(A3.31), A9.5(A9.5), A16.1(A17.1), and A17.1(A18.1).

All numbered exercises are from the textbook; exercises which start with ‘A’ are from the set of additional exercises posted on the textbook website. Numbers refer to March 11, 2015 version (numbers in parenthesis refer to January 7, 2019 version). 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

To pass the course, at least 50 % of the exercises must be done. There is also a 48 hour take-home exam that will take place early February.

### 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: TBD
- Project report (small, informal), deadline: TBD
- Project presentation (10 min): TBD