Continuous Optimisation (2017)

  • If you plan to attend the Continuous Optimisation Exam on Monday 15th January 2018, then please fill in the sign-up form as soon as possible (by Thursday 11th January 2018 at the latest).
  • CO_Dickinson_combined_v2017_09_18.pdf
    • This is a combined pdf of all the slides. You are allowed to take a print out of these slides (or a selection of them) into the exam. You are also allowed to highlight them.
    • YOU ARE NOT ALLOWED to add any extra notes, words or pictures to them.
    • YOU ARE NOT ALLOWED to take any other print outs in to the exam , so no print outs of the homework solutions nor the recommended literature.
    • If you find an error in this pdf then please let me know as soon as possible.
  • Exam Rules

Mastermath website:

Videos of some of the lectures are available at Due to a technical problem, only part of the lecture from week 41 (09/10/17) could be recorded.

Course material
There is no compulsory literature for this course as lecture slides/notes will be provided which contain all the information necessary to pass the course. Details of recommended literature is available on the course page of the mastermath website,

The student should have a solid bachelor level knowledge of linear algebra and multivariate analysis. The student should also have knowledge of linear optimisation and convex analysis to the level of being able to follow the text and do the exercises from the following:
  • Linear Programming, A Concise Introduction, Thomas S. Ferguson:
    Available at
    Chapters 1 and 2, along with the accompanying exercises.
  • Convex Optimization, Stephen Boyd and Lieven Vandenberghe:
    Available at
    Sections: 2.1, 2.2 and 3.1.
    Exercises (from the book): 2.1, 2.2, 2.12, 3.1, 3.3, 3.5 and 3.7

Final versions of the slides from the course will be available here after the lectures. The chapter/slide numbers do not correspond to the lectures (one chapter may take multiple lectures):
Chapter 1, (v2017-09-18);
Chapter 2, (v2017-09-28);
Chapter 3, (v2017-10-06);
Chapter 4, (v2017-10-09);
Chapter 5, (v2017-12-17);
Chapter 6, (v2017-11-06);
Chapter 7, (v2017-11-10);
Chapter 8, (v2017-11-28);
Chapter 9, (v2017-11-28);
Combined Slides (v2017-09-18);
Exam Rules

Homework exercises will be provided during the lectures. These will not be marked. It is recommended to try to answer the questions without looking at the answers in order to familiarise yourself with the course. You can then check your answers and if you are unsure of anything then you can ask during the following lecture or post your question on the student forum for the course on the Mastermath website:
Chapter 1:   Questions (v2017-09-12);   Answers (v2017-09-12);
Chapter 2:   Questions (v2017-09-12);   Answers (v2017-09-14);
Chapter 3:   Questions (v2016-10-10);   Answers (v2016-11-14);
Chapter 4:   Questions (v2017-10-05);   Answers (v2017-10-05);
Chapter 5:   Questions (v2016-10-31);   Answers (v2016-11-09);
Chapter 6:   Questions (v2017-11-13);   Answers (v2017-11-13);
Chapter 7:   Questions (v2017-11-10);   Answers (v2017-11-10);
Chapter 8:   Questions (v2017-11-17);   Answers (v2017-11-17);
Chapter 9:   Questions (v2016-11-18);   Answers (v2016-11-25);

Weekly summary
wk Class up to Homework up to
37 Chpt 1, slide 24 (Gauge Function) Prerequisites and 1.8
38 Chpt 1, end 1.16
39 Chpt 2, end 2.7
40 Chpt 3, slide 19 (Concluding KKT conditions) 3.3
41 Chpt 4, slide 16 (Strong duality proof, part III) 4.7
42 Chpt 4, end 4.12
43 Chpt 5, end 5.6
45 Chpt 6, end 6.5
46 Chpt 8, slide 8 (Example after Basic Properties) 8.2
47 Chpt 8, part way through slide 28 (Equivalent condition to Slater) 8.7
48 Chpt 9, end 9.6 and
Practice Exam 4
This course takes place at the University of Utrecht, De Uithof on Mondays from 13:15 until 15:00. The schedule is below, which is available as a google calendar which you can sync with. Events may be subject to change, and in the event of disagreement with the schedule on the mastermath website: please let me know in the discussion forum and trust the website, as it will probably just be an error on google calendar.

Practice Exams
Practice Exam 1:   Questions (v2016-11-21);   Answers (v2016-11-22)
Practice Exam 2:   Questions (v2016-12-05);   Answers (v2016-12-05)
Practice Exam 3:   Questions (v2016-11-22);   Answers (v2016-11-22)
Practice Exam 4:   Questions (v2017-11-29);   Answers (v2017-12-17)
Practice Exam 5:   Questions (v2017-11-24);   Answers (v2017-11-24)


The course will be assessed by a final written exam (and a retake).

In the case of a retake examination, the OER of the student's university determines the calculation of the final mark (e.g. highest, last or average).

If you are unable to attend both the main exam and the retake, then please get in contact with me as soon as possible. We will then attempt to find a solution to this problem.

The main exam for Continuous Optimisation will take place on Monday 15th January 2018, with the retake being on Monday 19th February 2018. Both of the exams will be in Utrecht from 13:30 until 16:30. Due to personal circumstances I may not be able to invigilate the exam myself. In this event a colleague will be found to replace me.

You may have noticed that the exams take place this year at a slightly different time to last year. However during the year previous to this the exams were again at a slightly different time. This is unfortunate but inevitable when things have to be arranged with multiple universities. I hope that this has not been a problem for too many people.
If you are only able to attend one of the exams then this single exam will have to suffice (unless you have a very good reason which you notify me of as soon as possible). My justification for this policy is as follows:

  • Suppose you cannot attend the main exam as you assumed that it would be at the same time as last year. As the main exam this year is at around the same time as the retake was last year, this means that you cannot have intended to attend the retake. It is thus sufficient for you to do as already planned, and only have one attempt at the exam. This one attempt would be the 'retake' on Monday 19th February 2018. Although this is unfortunately a significant amount of time after the end of the course, there are videos of the course online to help with revising for the exam.
  • Suppose you cannot attend the main or retake for another reason. The (preliminary) date of the main and retake exam were announced on the website at the start of the course, which was respectively over 4 and 5 months before the exams takes place. I consider this to be plenty of notice for the exams.
I apologise if anyone is disappointed with this policy and ask them to get in contact with me if they disagree with it (and have a good argument against it).

Exam rules
  • The final exam and the retake will be written exams.
  • The final exam will be on Monday 15th January 2018, 13:30 - 16:30 in Hall Alfa in the Educatorium, De Uithof, Utrecht.
  • The retake exam will be on Monday 19th February 2018, 13:30 - 16:30, location to be announced.
  • Those with extra time will take the exam in a different location and should have been informed about this by the Mastermath secretary, Samira van der Loo ( If you have not received an email from her, then make sure you contact her as soon as possible.
  • You should be at the exam room at least 15 minutes in advance, however I recommend that you plan on getting there much earlier than this in case of problems with the trains, etc.
  • If you wish, you may leave the exam early between 14:15 and 16:15, provided you can leave without disturbing anyone.
  • You are allowed to take a printed copy of the slides to the exam. I will provide a pdf of the final versions of all the slides for this nearer to the exam. You may highlight the slides, but you are not allowed to add any additional notes. You may not bring in any extra notes (so no homework solutions nor books).
  • The exam will be on the lecture slides and the homework exercises. The related course material was to give you a more rounded view on the course, however anything in the course material which is not covered in the slides or homework will not be tested.
  • During the exam: no calculators are allowed and mobile phones must be switched off.
  • There is to be no communicating with fellow students at any time either in the room or directly outside it. This includes before or after the exam, and also includes making hand signals.
  • Put your hand up if you have a question, want to hand in your exam early or wish to go to the toilet. Between 14:15 and 16:15 one student at a time will be allowed to go to the toilet.
  • If you are running late, make sure you send me an email detailing why you are late, when you expect to arrive and evidence (e.g. a photo).