# Convex Optimization

## FRT015F

#### Graduate course (7.5 ECTS credits) given at the Department of Automatic Control

January to March, 2013

First exercise meeting Jan 31 2013, 10.15-11.00 in M2498 (seminar room)

Organizer: Bo Bernhardsson, bob@control.lth.se, send me an email to be added to the mail list.

Meetings: Thursdays 10.15-12.00, see schedule below

Lectures:  Online video lectures by Stephen Boyd are available here. The participants should view roughly two of these video lectures per week (more first weeks). There will be no separate lectures held in Lund, we will focus entirely on exercise sessions.

#### Text book

The text book by Stephen Boyd and Lieven Vandenberghe is published by Cambridge University Press, who also makes it freely available for download. We are grateful to the book authors for generous support during the preparation of this course.

Schedule (numbers in paranthesis refer to Boyd lecture slides). I followed the 2007-08 videos, but there is also an alternative from 2010-11

• 31 jan (1-3.1): Introduction. Convex sets. Convex functions.
• 7 feb (3.2-4.34): Convex optimization problems
• 14 feb (4.35-5.17): Duality. [PontusG]
• 21 feb (5.18-6): Duality. Approximation.
• 28 feb (7-8.8): Statistical estimation. Geometric problems.
• 7 mar (8.8-9): Geometric problems. Numerical Linear Algebra
• 14 mar (10-11.10): Unconstrained minimization. Equality constrained minimization
• 21 mar (11.6-12.17): Equality constrained minimization. Interior-point methods.
• 28 mar (12.18-13) Interior-point methods.

#### Exercises and Handins

Before exercises fill in this Exercise_list

Exercise schedule: At meetings the participants should show and discuss solutions to the exercises. The meetings are held in the Automatic Control seminar room, unless otherwise stated. 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.

• 31 jan: 2.4, 2.8, 2.10, 2.12, 2.20, 3.2, 3.16, 3.18. Hint for 2.12 (d). Also do the quizzes.
• 7 feb: 3.3, 3.12 .3.20ab,3.22ab 3.34,3.36ad,3.38, 4.3,4.14,4.21, A3.3. Also scan the CVX manual.
• 14 feb: 4.33, 4.38,4.43ab, 4.57, 5.1,5.5,5.12,5.20,5.21,A10.2, A16.9
• 21 feb: 5.27, 5.35, 5.39, 5.43, 6,2 6.3ad, 6.8a, 6.9, A4.10abd (in d you need only  do (i), (ii) and (iii))
• 28 feb: 7.1, 7.3, 7.9, 7.10, 8.7, 8.11, 8.16, 8.21, A5.6, A5.10 (hint: Lasso)
• 7 mar: 8.26, A6.6, A7.3, A7.8, A7.10, A7.12, A7.13,  A6.4, A6.5
• 14 mar: 9.1, 9.5 (with alpha<1/2), 9.11, 9.30, 9.31, 10.1a, Handin7
• 21 mar: 10.3a, 10.5, 10.8, 10.12a, 10.15, A9.5a,b
• 28 mar: 11.2, 11.6, 11.7, A9.1 (no handin this week)

The A-exercises(such as A3.3) refer to Boyd/Vandenberghe's additional exercises available here and data files for these here. You might find the CVX example library useful also.

#### Software

You should make sure you have installed and can use CVX.

#### 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 exam can be started in the period [April 2-April 22]. It is a 48 hour take-home exam.

### 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