TMA947/MMG621, Nonlinear optimisation, 2018/19

Welcome to the course homepage for TMA947/MMG621: Nonlinear Optimisation.

The first lecture will be on Tuesday 4/9 at 15.15 in Pascal. The full schedule for the course can be found here.

For PhD students from other departments (not MV): To register to the course go to and apply for the course MMG621.

Latest news

19/11: The exam review is scheduled for Friday 23/11 at 12.00 in MVL13
01/11: Uploaded exam and exam solutions from 2018-11-01.
26/10: Added notes for Course summary
23/10: IMPORTANT! There is an exercise session on Wednesday 24/10 15-17 in Euler where Edvin Åblad will go through an old exam.
17/10: IMPORTANT! A course summary lecture is schedules for Thursday 25/10 15-17 in KA.
17/10: Added notes for Lecture 14
15/10: Added notes for Lecture 12 and Lecture 13
11/10: IMPORTANT: The exercise on Friday 12/10 has been moved the to Wednesday 17/10 at 15-17 in MVF23 and MVF31. The assignment exercises should, however, be presented on Monday 15/10!
5/10: Added notes for Lecture 10 and Lecture 11
1/10: Added notes for Lecture 8 and Lecture 9
1/10: Uploaded the PM for project part 2 and necessary AMPL-files Belgium.mod, Belgium.dat and
18/9: Added poll for Computer Exercise 1
11/9: Added notes for Lecture 5, Lecture 6, and Lecture 7
10/9: Added notes for Lecture 3 and Lecture 4
23/8: Added Course PM
23/8: Added notes for Lecture 1 and Lecture 2
23/8: Added exercise schedule.
23/8: Added lecture schedule.
23/8: Updated the course homepage.


Emil Gustavsson
Lecturer and course responsible
Business area leader within Machine Learning, Data Science, Optimization
Fraunhofer-Chalmers Centre

Michael Patriksson
Professor of applied mathematics, Mathematical Sciences
Email:, Tel: 772 5329, Room: L2084

Quanjiang Yu
Exercise assistant
Ph.D. student, Mathematical Sciences
Email:, Tel: 772 1094, Room: L2033

Edvin Åblad
Exercise assistant
Ph.D. student, Mathematical Sciences and Fraunhofer-Chalmers Centre

Course literature

An Introduction to Continuous Optimization, 3rd Edition
N. Andréasson, A. Evgrafov, E. Gustavsson, Z. Ned?lková, M. Patriksson, K.C. Sou, and M. Önnheim
Published by Studentlitteratur 2016 and found in the Cremona book store



The program is preliminary. Chapter numbers refer to the course book
Lecture Date Chapter Contents
1  4/9
1--2  Course presentation, introduction to optimization, notations, classification
2  6/9
3  Convex sets, convex functions, convex problems
3  10/9  4  Introduction to optimality conditions 
4  11/9  11  Unconstrained optimization algorithms 
5  17/9  5.1--5.4  Optimality conditions 
6  18/9  5.5--5.9  Optimality conditions 
7  24/9  6  Lagrangian duality 
8  25/9  7--8  Introduction to linear programming 
9  1/10  9  Linear programming 
10  2/10  10  Linear programming duality 
11  8/10  3, 4.4, 6.4  Convex optimization 
12  9/10  ---  Integer programming 
13  15/10  12  Feasible direction methods 
14  16/10  13  Constrained optimization 
15  TBD  ---  Summary of the course


Exercises numbered EX.Y can be found in the exercise sets. Exercises numbered X.Y can be found in the book (3rd Edition).

For a translation of the exercise numbers for the 2nd Edition of the course book, see the previous year, which can be found here
Exercise Date Assignment exercises Exercises Teacher exercises
1  7/9 ---  E1.2, E1.6--E1.9, 1.1, 1.2, 1.4  E1.1, E1.4, 1.3 
2  10/9 ---  3.1--3.3, 3.5, 3.7, 3.8, 3.10, 3.12--3.14, 3.16--3.19  3.4, 3.6, 3.9, 3.11, 3.15 
3  14/9 E1.3, E1.5, E1.10, E1.11  4.2, 4.3, 4.4, 4.5, 4.12, 4.15, 4.16  4.1, 4.4b, 4.6,  
4  17/9 ---  11.3, 11.6, 11.9, 11.11, 11.13  4.13, 11.5, 11.7, 11.4 
5  21/9 E2.5, E2.7, E2.8, 11.2  5.1, 5.3--5.10, 5.12, E3.1, E3.2, E3.4, E3.6  5.2, E3.3 
6  24/9 ---  E3.8, 6.1--6.3, 6.5--6.9, 6.11--6.12  5.11, E3.7, 6.4, 6.10 
7  28/9 E3.5, E3.9, E3.10, E3.11  8.2--8.5, 8.7, E4.1, E4.4  8.1, E4.2 
8  1/10 ---  9.2--9.3, 9.5--9.6, E4.6, E4.8--E4.11  8.6, 9.1, 9.4 
9  5/10 E4.3, E4.5, E4.7, E4.12  10.1-10.12,10.14-10.17, E5.4, E5.6, E5.8  E5.1, E5.2, 10.13 
10  8/10 ---  E5.10, E5.12, Section 6.4.2 in the course book  E5.9, E5.13 
11  12/10 E5.3, E5.5, E5.7, E5.11  12.1--12.3, 12.5--12.14  12.4, E6.4 
12  15/10 ---  13.1--13.4, 13.6--13.8  13.3, 13.5 
13  19/10 E6.1, E6.2, E6.5, E6.6  ---  --- 
14  TBD ---  ---  Old exam 

Computer labs

Students are supposed to attend one of the sessions for each computer exercise.
Poll for Computer Exercise 1

Exercise Date Contents
1  20/9 Steepest descent, Newton's method, Levenberg-Marquardt 
1  27/9 Steepest descent, Newton's method, Levenberg-Marquardt 
AMPL 4/10 Students test AMPL and can ask teachers for help
2  11/10 Penalty methods, KKT conditions 
2  18/10 Penalty methods, KKT conditions 

Computer labs

Computer exercise 1:
Exercise PM
Exercise files

Computer exercise 2:
Exercise PM
Exercise files

Assignments exercises

In order to get bonus points for the exam, a number of assignment exercises should be solved. These are to be prepared by the students for the exercise session in order to obtain a mark (one of the students who has prepared the assignment exercise will be chosen to demonstrate it on the blackboard). The assignment exercises for each exercise session can be found in the program above.

There will be in total 24 assignment exercises.

Note 1: If you mark an assignment exercise and are chosen to demonstrate it on the blackboard and have not prepared it, you will lose all of your marks.

Note 2: The bonus points obtained through the assignment exercises are valid one year.


Project part 1:
The aim of this part is to introduce you to mathematical modelling. The Deadline for handing in the report is 26/9 and it should be done through PingPong.
Project part 1, PM

Project part 2:
The aim of this part is to introduce you to AMPL. Deadline for handing in the report is 10/10 and it should be done through PingPong.

Project part 2, PM

The necessary AMPL-files are: Belgium.mod, Belgium.dat, and

An introduction to AMPL can be found here.
Handing in:
The model assignment is handed in through PingPong in pdf format only!
In order to hand in, go to ''Project groups'' in PingPong and create a group called ''name1_name2'' (or ''name1'', if only one group member). Read - and follow! - the instructions on what to include in the report before you hand it in.
No more than two persons per group; the report must include on the first page the names of each group member, and the e-mail address of at least one group member.


Writing tools:
Prefarably Latex but other wordformatting tools are also ok (such as word, etc) as long as the report is readable as pdf.

Student representatives

The student representatives for the course are:
Marios Aspris (
Karl-Rehan Chiu Falck (
Nina Malmqvist (
Benjamin Midtvedt (
Jens Nilsson (


A written exam worth 6.0 credits will be held the 1/11 at 14.00--19.00. The maximum points on the exam is 21 and the limits are as follows.
Chalmers: 3: 10, 4: 14, 5: 18
GU: G: 10, VG: 16
Passed on one question requires 2 points of 3. To pass requires 10 points and three passed questions.

Computer exercises:
The two computer exercises are mandatory.

Assignment exercise:
The assignment exercises can give up to 2 bonus points for the exam. The bonus points are valid one year after the points are collected.

A passed project will give 1.5 credits.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Old exams

2018-08-21 Exam Answers
2018-04-05 Exam Answers
2017-08-24 Exam Answers
2017-01-10 Exam Answers
2016-08-25 Exam Answers
2016-04-05 Exam Answers
2016-01-12 Exam Answers
2015-08-27 Exam Answers
2015-04-14 Exam Answers
2015-01-13 Exam Answers
2014-04-22 Exam Answers
2013-12-17 Exam Answers
2013-08-29 Exam Answers
2012-12-17 Exam Answers
2012-04-10 Exam Answers
2011-12-12 Exam Answers
2011-04-26 Exam Answers
2010-12-13 Exam Answers
2010-04-06 Exam Answers
2009-08-27 Exam Answers
2009-04-14 Exam Answers
2008-08-28 Exam Answers
2008-03-25 Exam Answers
2007-12-17 Exam Answers


Course PM
List of theorems (3rd Edition of the book)
List of theorems (2nd Edition of the book)
Errors in the course book (3rd Edition of the book)
Index (3rd Edition of the book)
AMPL intro

Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 10
Lecture 11
Lecture 12
Lecture 13
Lecture 14

Exercise set 1
Exercise set 2
Exercise set 3
Exercise set 4
Exercise set 5
Exercise set 6

Computer exercises:
Computer exercise 1, PM
Computer exercise 1, files
Computer exercise 2, PM
Computer exercise 2, files

Project part 1, PM
Introduction to AMPL
Project part 2, PM