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FSF3847 Convex Optimization with Engineering Applications 6.0 credits

Course memo Spring 2021-1

Version 10 – 03/24/2021, 11:50:17 AM

Course offering

Spring 2021-1 (Start date 22/03/2021, English)

Language Of Instruction

English

Offered By

SCI/Mathematics

Course memo Spring 2021-1

Course presentation

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

Course contents

  • 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

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.

Learning activities

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.

Detailed plan

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 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

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:

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.

Course registration

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.

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

Round Facts

Offered By

SCI/Mathematics

Language Of Instruction

English

Course offering

Spring 2021-1 (Start date 22/03/2021, English)