2E5295/5B5749 Convex optimization with engineering applications, 4p/8p

General information

This course is a graduate course, given jointly by the Department of Signals, Sensors and Systems, and the Department of Mathematics at KTH within the framework of the Graduate School of Telecommunications (GST). This is an 'accelerated program course', which can be included in the first degree (civilingenjörsexamen, Master of Science) as well as in a graduate degree if you decide to pursue a Licentiate or Doctorate Degree. Note that the course is primarily not intended for students with focus on optimization, but rather aimed for students from other areas.

Examiners: Mikael Johansson (EE), Anders Forsgren (Mathematics)

The course consists of 24h lectures, given during Period 2, 2006.

Course literature: S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004, ISBN: 0521833787

Aim

After completed course, you will be able to

characterize fundamental aspects of convex optimization
(convex functions, convex sets, convex optimization and duality);
characterize and formulate linear, quadratic, geometric and semidefinite programming problems;
implement, in a high level language such as Matlab, crude versions of modern methods for solving convex optimization problems, e.g., interior methods;
solve large-scale structured problems by decomposition techniques;
give examples of applications of convex optimization within statistics, communications, signal processing and control.

Syllabus

Convex sets
Convex functions
Convex optimization
Linear and quadratic programming
Geometric and semidefinite programming
Duality
Smooth unconstrained minimization
Sequential unconstrained minimization
Interior-point methods
Decomposition and large-scale optimization
Applications in estimation, data fitting, control and communications

Course requirements

There are two versions of the course, with different credits and requirements

The 4-credit version requires successful completion of home work assignments and the presentation of a short lecture on a special topic
The 8-credit version requires, in addition to the requirements above, the successful completion of a 72h take-home exam, as well as a short optimization project related to your own research.

There will be a total of four sets of hand-ins distributed during the course. Late homework solutions are not accepted.

The short lecture should sum up the key ideas, techniques and results of a (course-related) research paper in a clear and understandable way to the other attendees. The presentation should be limited to 10 minutes.

For the 8-credit course, we encourage you to come up with a optimization-related research problem in your own research area. The results should be summarized in a short research report.

Prerequisites

The course requires basic knowledge of calculus and linear algebra. Please contact the lecturers if you are uncertain about your prereuisities.

Schedule

Lectures will be given in Room 3721, Lindstedtsvägen 25, KTH.

Lecture	Date	Time	Venue	Activity	Lecturer
1	Wed Oct 25	10-12	Room 3721	Introduction (pdf)	MJ
2	Tue Oct 31	13-15	Room 3721	Convexity (pdf, 1 per page) (ps, 4 per page)	AF
3	Thu Nov 2	13-15	Room 3721	Linear programming and the simplex method (pdf, 1 per page) (ps, 4 per page)	AF
4	Tue Nov 7	13-15	Room 3721	Linear programming, Lagrangian relaxation and duality (pdf, 1 per page) (ps, 4 per page)	AF
5	Thu Nov 9	13-15	Room 3721	Convex programming and semidefinite programming (pdf, 1 per page) (ps, 4 per page)	AF
	Tue Nov 14			(No lecture)
	Thu Nov 16			(No lecture.) Please attend seminar by Stephen Boyd.
6	Tue Nov 21	13-15	Room 3721	Sensitivity and multiobjective optimization	MJ
7	Thu Nov 23	13-15	Room 3721	Geometric programming and second-order cone programming	MJ
8	Tue Nov 28	13-15	Room 3721	Smooth convex unconstrained and equality-constrained minimization (pdf, 1 per page) (ps, 4 per page)	AF
9	Thu Nov 30	13-15	Room 3721	Interior methods (pdf, 1 per page) (ps, 4 per page)	AF
10	Tue Dec 5	13-15	Room 3721	Decomposition and large-scale optimization (pdf)	MJ
11	Wed Dec 6	15-17	Room 3721	Applications in communications and control (pdf)	MJ
12	Tue Dec 12	13-15	Room 3721	Applications in communications and control (pdf)	MJ

Please note that the schedule is preliminary!