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.
Course memo Spring 2023
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Course presentation
Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Spring 2019
Content and learning outcomes
Course contents
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Convex sets
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Convex functions
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Convex optimization
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Linear and quadratic programming
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Geometric and semidefinite programming
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Duality
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Smooth unconstrained minimization
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Sequential unconstrained minimization
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Interior-point methods
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Decomposition and large-scale optimization
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Applications in estimation, data fitting, control and communications
Intended learning outcomes
After completed course, the student should be able to
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characterize fundamental aspects of convex optimization (convex functions, convex sets, convex optimization and duality);
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characterize and formulate linear, quadratic, geometric and semidefinite programming problems;
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implement, in a high level language such as Matlab, crude versions of modern methods for solving convex optimization problems, e.g., interior methods;
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solve large-scale structured problems by decomposition techniques;
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give examples of applications of convex optimization within statistics, communications, signal processing and control.
Learning activities
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 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.
Detailed plan
| 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 homework assignments
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.
Research presentation day
The presentations of a short lecture on a special topic, specified in Examination and Completion below, will be held on Tuesday May 16.
Preparations before course start
Literature
Course literature: S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004, ISBN: 0521833787
Support for students with disabilities
Students at KTH with a permanent disability can get support during studies from Funka:
Course registration
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.
Examination and completion
Grading scale
P, F
Examination
- INL1 - Assignment, 6.0 credits, Grading scale: 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.
Other requirements for final grade
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.
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
No information inserted
Contacts
Course Coordinator
Teachers
Examiner
Round Facts
Start date
20 Mar 2023
Course offering
- Spring 2023-60827
Language Of Instruction
English