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EL3300/SF3849 Convex optimization with engineering
applications, 6cr
General information
This course is a graduate course, given jointly by the School of
Electrical Engineering, and the Department of Mathematics at KTH. The
course is primarily not intended for students with focus on
optimization, but rather aimed for students from other areas.
Examiners: Anders
Forsgren
(Mathematics), Mikael
Johansson (Automatic
Control), Jeffrey Larson
(Automatic Control),
The course consists of 24h lectures, given during Period 2, 2012.
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 is one version of the course given this time, the 6-credit
version
- The 6-credit version requires successful completion of home work
assignments and the presentation of a short lecture on a special topic
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.
Prerequisites
The course requires basic knowledge of calculus and linear algebra.
Please contact the lecturers if you are uncertain about your prerequisities.
Schedule
Lectures will be given in Room 3721, Lindstedtsvägen 25, KTH.
| Lecture |
Date |
Time |
Venue |
Activity |
Lecturer |
| 1 |
Tue Oct 23 |
13-15 |
Room 3721 |
Introduction
(pdf) |
MJ |
| 2 |
Thu Oct 25 |
13-15 |
Room 3721 |
Convexity
|
JL |
| 3 |
Tue Oct 30 |
13-15 |
Room 3721 |
Linear programming and the simplex method
|
JL |
| 4 |
Thu Nov 1 |
13-15 |
Room 3721 |
Lagrangian relaxation, duality and optimality for
linearly constrained problems
(pdf)
|
AF |
| 5 |
Tue Nov 6 |
13-15 |
Room 3721 |
Convex programming and semidefinite programming
(pdf) |
AF |
| 6 |
Thu Nov 8 |
13-15 |
Room 3721 |
Geometric programming and second-order cone programming
|
JL |
| 7 |
Tue Nov 13 |
13-15 |
Room 3721 |
Sensitivity and multiobjective optimization
|
JL |
| 8 |
Thu Nov 15 |
13-15 |
Room 3721 |
Smooth convex unconstrained and equality-constrained minimization
(pdf)
|
AF |
| 9 |
Thu Nov 22 |
10-12 |
Room 3721 | Interior methods
(pdf)
|
AF |
| 10 |
Thu Nov 22 |
13-15 |
Room 3721 |
Decomposition and large-scale optimization
|
MJ |
| 11 |
Tue Nov 27 |
13-15 |
Room 3721 |
Applications in communications and control
| MJ |
| 12 |
Thu Nov 29 |
13-15 |
Room 3721 |
Applications in communications and control |
MJ |
Course web page
http://www.math.kth.se/optsyst/forskning/forskarutbildning/SF3849/
Optimization and Systems Theory, KTH
Anders Forsgren, andersf@kth.se
|