# 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);

### 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 will be a written open-book exam. Please register yourself in Osiris for taking part in the exam. For the exam, you can bring the book (or a print-out of the pdf), copies of the slides,**and a cheat sheet (1 page)**. No other written notes or 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 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 **January 14, 2024**.
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 ** December 4, 2023**. 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

prof.dr.ir. Geert Leus (GL), dr.ir. Borbala (Bori) Hunyadi (BH) and ir. Alberto Natali (AN) .

### Online Lectures

The Collegerama recordings can be access here.

## Schedule

The schedule for 2023-2024 is as follows. Classes are on Wednesdays (15.45 - 17.30) and Fridays (10.45 - 12.30).

Date | Book | Slides | Video | |||
---|---|---|---|---|---|---|

1. | Wed 15 Nov | AN | Recap linear algebra concepts | Linear algebra slides | Lect. 1 | |

2. | Fri 17 Nov | GL | Introduction (functions, sets, optimization basics) | Ch.1 and Appendix A of the textbook | Ch.1 slides | Lect. 2 |

3. | Wed 22 Nov | BH | Convex sets and functions | Ch.2 and Ch. 3 | Ch.2 and 3 slides | Lect. 3 |

4. | Fri 24 Nov | GL | Convex sets and functions | Ch.2 and Ch. 3 | Ch.2 and 3 slides | Lect. 4 |

5. | Wed 29 Nov | BH | Unconstrained minimization | Ch. 9.1-9.5 | Ch.9 slides | Lect. 5 |

6. | Fri 1 Dec | NO CLASS | ||||

7. | Wed 6 Dec | GL | Canonical problems (LP, QP, SDP) | Ch.4 | Ch.4 slides | Lect. 6 |

8. | Fri 8 Dec | GL | Duality | Ch. 5 | Ch.5 slides | Lect. 7 |

9. | Wed 13 Dec | GL | Constrained minimization |
Ch. 10.1, 10.2, 11.1, 11.2 |
Ch.10 and Ch. 11 slides | Lect. 8 |

10. | Fri 15 Dec | AN | Convex-Cardinality problems | Cardinality slides | Lect. 9 | |

11. | Wed 20 Dec | BH | Subgradient methods | Subgradients | Subgradient methods slides | Lect. 10 |

12. | Fri 22 Dec | BH | Subgradient methods | Subgradients | Subgradient methods slides | Lect. 11 |

13. | Wed 10 Jan | GL/BH/AN | Exercises | Exercises slides | Matlab codes | Lect. 12 |

14. | Fri 12 Jan | GL/BH/AN | Exercises | N/A | Lect. 13 | |

Sun 14 Jan | Deadline lab assignment report | |||||

15. | Wed 17 Jan | GL/BH/AN | Projects | Online | N/A | |

16. | Fri 19 Jan | GL/BH/AN | Projects | online | N/A | |

Thu 25 Jan 2024 | Exam 13.30-16.30 |

### 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.### Previous exams

Solutions of January 2023.

Solutions of April 2022.

Solutions of January 2022.

Solutions block 1 Solutions block 2 of April 2021.

Solutions block 1 Solutions block 2 of January 2021.

Solutions of January 2020.