Introduction

The 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);
The course includes a take-home lab assignment (size 1 EC = 28 hours) which can be done in groups of 2 students. Several track-dependent assignments are offered.

Preliminary knowledge

To follow the course with profit, you will need the working knowledge of linear algebra and calculus with functions in multiple variables.

Exam

The 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.

Projects

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.

Project 1: Change Detection in Time Series Model. Dataset

Project 2: Linear Support Vector Machines. Dataset

Project 3: Multidimensional Scaling for Localization. Dataset

Project 4: MIMO Detection. Dataset

Project 5: Compressed Sensing. Dataset.

Book

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

Instructors

ir. Mario Coutino (MC) and prof.dr.ir. Geert Leus (GL).

Online Lectures

The Collegerama recordings can be access here.

Schedule

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.


Date

Book Slides Video
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

Subgradient methods slides Lect. 10
Sun 5 Jan Deadline lab assignment report
11. Thur 9 Jan GL & MC Subgradient methods Subgradients

Subgradient methods

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 Projects13.45-15.30 EWI-Ampere Lect. 13
14. Wed 14 Jan MC & GL Projects10.45-12.45 EWI-Chip Lect. 14
Wed 22 Jan 2020 Exam 13.30-16.30 EWI-Lecture Hall F & G

Exercises

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 excercises

Here 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.

Homework 1.

Homework 2.

Homework 3.

Homework 4.

Homework 5.

Previous exams

Solutions of January 2019.

Solutions of April 2018.

Exam and Solutions of January 2018.

Exam and Solutions of April 2017.

Exam and Solutions of January 2017.

Old Syllabus

Exam and Solutions of April 2016.

Exam and Solutions of January 2016.