Convex 2012



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

January to March, 2012

Organizer: Bo Bernhardsson

Meetings: Wednesdays  13.15-15.00 labC.

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
  • Feb 1 (1-3.1): Introduction. Convex sets. Convex functions.
  • Feb 8 (3.2-4.34): Convex optimization problems.
  • Feb 15 (4.35-5.17): Duality.
  • Feb 22 (5.18-6): Duality. Approximation.
  • Feb 29 (7-8.8): Statistical estimation. Geometric problems.
  • Mar 7 (8.8-9): Geometric problems. Numerical Linear Algebra
  • Mar 14 (10-11.10): Unconstrained minimization. Equality constrained minimization
  • Mar 21 (11.6-12.17): Equality constrained minimization. Interior-point methods.
  • Mar 28 (12.18-13) Interior-point methods.

Exercises and Handins

Exercise schedule: At meetings the participants should show and discuss solutions to the exercises. The meetings are held in the Automatic Control labC in the M-building. The handins, in bold face below, should be done individually and handed in at the exercise session.

  • Feb 1: 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.
  • Feb 8: 3.3, 3.12 .3.20ab,3.22ab 3.34,3.36ad,3.38, 4.3,4.14,4.21, A3.3.
  • Feb 15: 4.33, 4.38,4.43ab, 4.57, 5.1,5.5,5.12,5.20,5.21,A10.2, A16.9
  • Feb 22: 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))
  • Feb 29: 7.1, 7.3, 7.9, 7.10, 8.7, 8.11, 8.16, 8.21, A5.6, A5.10 (hint: Lasso)
  • Mar 7: 8.26, A6.6, A7.3, A7.8, A7.10, A7.12, A7.13,  A6.4, A6.5
  • Mar 14: 9.1, 9.5 (with alpha<1/2), 9.11, 9.30, 9.31, 10.1a, Handin7
  • Mar 21: 10.3a, 10.5, 10.8, 10.12a, 10.15, A9.5a,b
  • Mar 28: 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.


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


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 29th of March to 20th April 2012.It is a 48 hour take-home exam.

24 persons took the 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: March 23
  • Project report (small, informal), deadline: April 30, May 28
  • Project presentation (10 min): May 28 13.15, seminar room