IntroductionThe course covers several basic and advanced topics in convex optimization. The goal of this course is to recognize and formulate problems as convex optimization problems. There will be an emphasis on developing algorithms for moderate as well as large size problems. The course provides insights that can be used in a variety of disciplines including signal and image processing, machine learning, and control systems.
The course treats:
- Background and optimization basics;
- Convex sets and functions;
- Canonical convex optimization problems (LP, QP, SDP);
- First-order methods (gradient, subgradient);
- Second-order methods (unconstrained and constrained optimization);
Preliminary knowledgeTo follow the course with profit, you will need the working knowledge of linear algebra and calculus with functions in multiple variables.
ExamThe exam is written, open-book. For the exam, you can bring the book (or a print-out of the pdf) and copies of the slides. No written notes or other materials are allowed.
The lab assignment is completed with a compact report and 10 minute presentation. During the last two lectures, the students are expected to present their project to their colleague students. Passing the lab assignment is compulsory for the exam grade to become valid. Moreover, the assignment is graded and counts for about 20% of your final grade.
The course contains a compulsory lab assignment worth 1 EC (28 hours, 20% of your final grade). The assignment is done in groups of 2 students.
The deadline for submitting the reports is Sunday 5th Jan 2020. This deadline is "firm" and no deadline extensions will be granted. If you don't submit your report within this deadline you will not be allowed to present your project and you cannot pass this course.
Signing up for the lab assignment has to be done via Brightspace. To enroll, go to the "Collaboration" tab in Brightspace, and then select groups. Signing up can be done until November 29th 2019. To upload your report, go to assignments in Brightspace.
Stephen Boyd and Lieven Vandenberghe, "Convex Optimization", Cambridge University Press, 2004. The pdf version of this book is freely available and it can be found online here.
Slides are based on Convex Optimization course ee364a offered at Stanford University by Prof. Boyd
Instructorsir. Mario Coutino (MC) and prof.dr.ir. Geert Leus (GL).
The Collegerama recordings can be access here.
The schedule for 2019-2020 is as follows. Classes are on Thursdays between 13.45-15.45 and on Fridays between 10:45-12:30.
|1.||Thur 14 Nov||GL||Introduction (functions, sets, optimization basics)||Ch.1 and Appendix A of the textbook||Ch.1 slides||Lect. 1|
|2.||Fri 15 Nov||GL||Convex sets and functions||Ch.2 and Ch. 3||Ch.2 and 3 slides||Lect. 2|
|3.||Thur 21 Nov||GL||Convex sets and functions||Ch.2 and Ch. 3||Ch.2 and 3 slides||Lect. 3|
|4.||Fri 22 Nov||GL||Canonical problems (LP, QP, SDP)||Ch.4||Ch.4 slides||Lect. 4|
|5.||Thur 28 Nov||GL||Duality||Ch. 5||Ch.5 slides||Lect. 5|
|6.||Fri 29 Nov||GL||Unconstrained minimization||Ch. 9.1-9.5||Ch.9 slides||Lect. 6|
|7.||Thur 5 Dec||MC||Constrained minimization||
Ch. 10.1, 10.2, 11.1, 11.2
|Ch.10 and Ch. 11 slides||Lect. 7|
|8.||Fri 6 Dec||MC||Convex-Cardinality problems||Cardinality slides||Lect. 8|
|9.||Thur 12 Dec||MC||Exercises||Exercises slides||Matlab codes||Lect. 9|
|10.||Fri 13 Dec||MC||Subgradient methods||Subgradients||Subgradient methods slides||Lect. 10|
|Sun 5 Jan||Deadline lab assignment report|
|11.||Thur 9 Jan||GL & MC||Subgradient methods||Subgradients||Subgradient methods slides||Lect. 11|
|12.||Fri 10 Jan||AM||Dual decomposition methods for optimal network design||Optimal network design slides||Lect. 12|
|13.||Tue 13 Jan||MC & GL||Projects||13.45-15.30||EWI-Ampere||Lect. 13|
|14.||Wed 14 Jan||MC & GL||Projects||10.45-12.45||EWI-Chip||Lect. 14|
|Wed 22 Jan 2020||Exam 13.30-16.30 EWI-Lecture Hall F & G|
Note that the exams are open book, but you must be very familiar with the material to be able to solve the questions in time. Train by solving many exercise questions from the book.
The book (BV) contains many exercises. In addtion, some more excercises can be found here (AE). A pdf of the Solutions Manual can probably be found on the internet. Some suggested excercise problems can be found below.
|Chapter 2:||BV2.5; BV2.7; BV2.12; BV2.15; AE1.1; AE1.3|
|Chapter 3:||BV3.2; BV3.15; BV3.16; BV3.18; BV3.58; AE2.6|
|Chapter 4:||BV4.1; BV4.11; AE3.3; AE3.7; AE3.8; AE3.13|
|Chapter 5:||BV5.1; BV5.7; BV5.29; BV5.30; AE4.10; AE4.15; AE4.16|
Previous homework excercisesHere are the past homeworks of ee4530 although the content of ee4530 is different since 2016/17. The relevant ones can be used to train for the exam. The homeworks are, however, now replaced with the mini projects. So you don't have to turn them in.
Solutions of January 2019.
Solutions of April 2018.
Exam and Solutions of April 2016.
Exam and Solutions of January 2016.