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.
Content and learning outcomes
Linear and quadratic programming
Geometric and semidefinite programming
Smooth unconstrained minimization
Sequential unconstrained minimization
Decomposition and large-scale optimization
Applications in estimation, data fitting, control and communications
Intended learning outcomes
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
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.
|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|
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||10-12||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 homework assignments
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.
Research presentation day
The presentations of a short lecture on a special topic, specified in Examination and Completion below, will be held on Wednesday May 12.
Preparations before course start
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:
Please inform the course coordinator if you need compensatory support during the course. Present a certificate from Funka.
Examination and completion
- 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.
- 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.
No information inserted
Language Of Instruction
Spring 2021-1 (Start date 22/03/2021, English)