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EL3300/SF3847 Convex optimization with engineering
applications, 6cr
(The lecture notes will be updated during the course. They are not available yet.)
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)
and
Mikael
Johansson (Automatic
Control).
The course consists of 24h lectures, given during Period 2, 2016.
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
For passing the course, successful completion of homework
assignments and presentation of a research paper in a short lecture
are required.
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 notes can be found at the course's Canvas page.
| Lecture |
Date |
Time |
Venue |
Activity |
Lecturer |
| 1 |
Tue Nov 1 |
13-15 |
Room 3721 |
Introduction
|
AF/MJ |
| 2 |
Thu Nov 3 |
10-12 |
Room 3721 |
Convexity
|
AF |
| 3 |
Mon Nov 7 |
10-12 |
Room 3721 |
Linear programming and the simplex method
|
AF |
| 4 |
Thu Nov 10 |
10-12 |
Room 3721 |
Lagrangian relaxation, duality and optimality for
linearly constrained problems
|
AF |
| 5 |
Tue Nov 15 |
13-15 |
Room 3721 |
Sensitivity and multiobjective optimization
|
MJ |
| 6 |
Thu Nov 17 |
10-12 |
Room 3721 |
Convex programming and semidefinite programming
| AF |
| 7 |
Tue Nov 22 |
8-10 |
Room 3721 |
Geometric programming and second-order cone programming
|
MJ |
| 8 |
Thu Nov 24 |
10-12 |
Room 3721 |
Smooth convex unconstrained and equality-constrained minimization
|
AF |
| 9 |
Tue Nov 29 |
13-15 |
Room 3721 | Interior methods
|
AF |
| 10 |
Thu Dec 1 |
10-12 |
Room 3721 |
Decomposition and large-scale optimization
|
MJ |
| 11 |
Tue Dec 6 |
13-15 |
Room 3721 |
Applications in communications and control
| MJ |
| 12 |
Thu Dec 8 |
10-12 |
Room 3721 |
Applications in communications and control
| MJ |
Research paper presentations will be held on December 9.
Course web page
http://www.math.kth.se/optsyst/forskning/forskarutbildning/SF3847/
Optimization and Systems Theory, KTH
Anders Forsgren, andersf@kth.se
|