Course memo Spring 2023-60827
Version 2 – 03/16/2023, 9:09:23 AM
Spring 2023-1 (Start date 20/03/2023, 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 2023.
Lectures will be given in Room 3721, Lindstedtsvägen 25, KTH.
There will be four set of homeworks, including peer grading, and an oral presentation of a selected topic. Lecture notes, homework assignment and other material related to the course will be posted in Canvas.
Video recordings from the lectures when the course given in spring 2021 are available in Canvas, as a complement.
| L# | Date | Time | Venue | Topic | Lecturer |
|---|---|---|---|---|---|
| 1 | Tue Mar 21 | 13-15 | Room 3721 | Introduction | MB/AF/JJ |
| 2 | Fri Mar 24 | 13-15 | Room 3721 | Convexity | AF |
| 3 | Tue Mar 28 | 13-15 | Room 3721 | Linear programming and the simplex method | AF |
| 4 |
Fri Mar 31 |
13-15 | Room 3721 | Lagrangian relaxation, duality and optimality for linearly constrained problems | AF |
| 5 | Tue Apr 4 | 10-12 | Room 3721 | Sensitivity and multiobjective optimization | MB |
| 6 | Tue Apr 18 | 13-15 | Room 3721 | Convex programming and semidefinite programming | AF |
| 7 | Fri Apr 21 | 13-15 | Room 3721 | Smooth convex unconstrained and equality-constrained minimization | AF |
| 8 | Tue Apr 25 | 13-15 | Room 3721 | Conic programming, dual decomposition and subgradient methods | MB |
| 9 | Fri Apr 28 | 13-15 | Room 3721 | Interior methods | AF |
| 10 | Tue May 2 | 13-15 | Room 3721 | Large-scale optimization | JJ |
| 11 | Fri May 5 | 13-15 | Room 3721 | Applications | MB |
| 12 | Tue May 9 | 13-15 | Room 3721 | Applications | JJ |
Hand-in dates for the four homework assignments, specified in Examination and Completion below, are April 4, April 18, April 28 and May 9. 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 Tuesday May 16.
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:
PhD students from KTH register through regular registration procedures. Assistance can be obtained 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
