Course memo Spring 2021-61149
Version 7 – 02/01/2021, 3:21:37 PM
Spring 2021-1 (Start date 22/03/2021, English)
English
SCI/Mathematics
Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Spring 2019
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
After completed course, the student should 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.
The course consists of 24h lectures, given during Period 4, spring 2021.
Lectures will be given via Zoom, https://kth-se.zoom.us/j/68296620263
Lecture notes, homework assignment and other material related to the course will be posted in Canvas.
(There may be slight changes in the schedule. It is still preliminary.)
| L# | Date | Time | Venue | Topic | Lecturer |
|---|---|---|---|---|---|
| 1 | Wed Mar 24 | 13-15 | Zoom | Introduction | MB/AF/JJ |
| 2 | Fri Mar 26 | 13-15 | Zoom | Convexity | AF |
| 3 | Wed Mar 31 | 13-15 | Zoom | Linear programming and the simplex method | AF |
| 4 |
Wed Apr 7 |
13-15 | Zoom | Lagrangian relaxation, duality and optimality for linearly constrained problems | AF |
| 5 | Fri Apr 9 | 13-15 | Zoom | Sensitivity and multiobjective optimization | MB |
| 6 | Wed Apr 14 | 13-15 | Zoom | Convex programming and semidefinite programming | AF |
| 7 | Fri Apr 16 | 13-15 | Zoom | Smooth convex unconstrained and equality-constrained minimization | AF |
| 8 | Wed Apr 21 | 13-15 | Zoom | Applications of conic programming | MB |
| 9 | Fri Apr 23 | 13-15 | Zoom | Interior methods | AF |
| 10 | Wed Apr 28 | 13-15 | Zoom | Large-scale optimization | JJ |
| 11 | Fri Apr 30 | 13-15 | Zoom | Applications | MB |
| 12 | Wed May 5 | 10-12 | Zoom | Applications | JJ |
Hand-in dates for the four homework assignments, specified in Examination and Completion below, are April 7, April 16, April 23 and May 5. Late homework solutions are not accepted.
The presentations of a short lecture on a special topic, specified in Examination and Completion below, will be held on Wednesday May 12.
Course literature: S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004, ISBN: 0521833787
Students at KTH with a permanent disability can get support during studies from Funka:
Funka - compensatory support for students with disabilities
Please inform the course coordinator if you need compensatory support during the course. Present a certificate from Funka.
PhD students from KTH register through e-ISP and by sending e-mail to phdadm@math.kth.se.
PhD students from other universities must fill out this form and send signed copy by e-mail to phdadm@math.kth.se.
P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Successful completion of homework assignments and the presentation of a short lecture on a special topic.
There will be a total of four sets of homework assignments 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.
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English
