Course syllabus
The exams are corrected. The results can be found in the assignment "Exam" on the Canvas page for the exam.
NOTE: The number of points you received on the exam in Canvas is including bonus points.
The grade limits are:
Chalmers:
3: 10
4: 14
5: 18
GU:
G: 10
VG: 16
In order to pass the exam you also need to pass (have 2 or more points) at least 3 questions.
You will have the possibility to ask questions regarding the corrections on Tuesday 24/11 at 10-12 in a Zoom-meeting (link will be posted later)
Solution to the exam:
tentalosning_TMA947_201029-1.pdf
Course PM
Welcome to the course homepage for TMA947/MMG621: Nonlinear Optimisation.
This page contains the program of the course: lectures, exercise sessions and computer labs. Also other information, such as teachers, literature and examination, are included.
A separate course PM with more detailed information (including learning outcomes) can be found here
The TimeEdit schedule can be found here
Information regarding online examination
The exam will be posted in a separate course page here on Canvas that you should have access to if you are registered for the exam. This page is, however, not published yet. On that page you will find the link to the Zoom-meeting you should attend during the exam.
Specific information for this course:
- The content of the exam will be similar to previous exams
- One exception is that we will not ask you to prove any of the theorems in the theory list (found here on Canvas), However, the content of the theorems and propositions in the theory list are important to know and questions where these results can/should be used may be included.
- All aids are allowed except collaborations with other.
In order to take the exam you need to:
- Be submitted to the exam
- During to entire time be connected to the Zoom-meeting with the video turned on and with you in sight. You shall have your real name as the meeting name so that the exam supervisor can see this. You can connect with computer or with mobile phone. You need to be logged in with your CID in Zoom through https://chalmers.zoom.us/ (Links to an external site.) or with your GU-account through https://gu-se.zoom.us/ (Links to an external site.)
- Have your ID available during the exam. This should be displayed in the beginning of the exam. In order to control your ID you will be transfered to a breakout-room in Zoom where you will be asked to show your ID.
All aids are allowed, but it is forbidden to communicate with anybody during the exam. There for it is forbidden to:
- use any form of headsets or earphones.
- communicate in any form with people (except the examiner or exam supervisor)
- be in a room where more than one person is situated or in a room that is directly connected to another room without a door between. If this is not possible due to quarantine or any other reasons you need to in advance report this to the examiner.
During the exam:
- The Zoom meeting will open at least 15 minuted before the exam starts.
- The exam will be published in Canvas when the exam time starts.
- You will be invited to a breakout-room in Zoom in order to verify your identity.
- If you need to go to the restroom let the exam supervisor know this before you go and when you get back by writing messages in Zoom to the exam supervisor.
- The exam time is 5 hours.
- When the exam time is finished you should immediately start scanning your solutions. It is not allowed to continue working on the exam after the time is out. You have a maximum of 30 minutes for scanning and handing in the solutions in Canvas. Delayed submission will only be allowed if it is due to technical issues. If you use your mobile phone for scanning use scanning apps (e.g. CamScanner or Genius skanning/Genius scan). The solutions should be handed in as one pdf-file. Try the apps out before the exam so you know how to scan multiple sheets and setting them together as one pdf. As cover sheet you should scan an attest that you have folloed all rules and this sheet should be signed.
Before the exam you should:
- Get familiar with Zoom
- If you will use your mobile phone for scanning the solutions, please try the app before the exam so that you know how to scan and submit the solutions.
- Prepare a cover sheet where it says "I insure that I have answered the questions for the exam by myself and without help from anyone else" together with your signature.
Digital teaching
All teaching in this course will be performed digitally. No education will be performed on campus.
Lectures
The lectures will be pre-recorded and uploaded to Canvas. Lecture notes are available for all lectures and all notes taken by the lecturer during the lectures will also be available.
Exercise
The exercises will be held online in Zoom at the time slots given in the schedule. Links to the Zoom-meetings will be posted here on Canvas.
Each exercise class has two scheduled times, so got to either Mondays 10-12 or Tusdays 10-12 and either Thursdays 13:15-15 or Fridays 8-10.
Link to Edvins session: https://chalmers.zoom.us/j/65476823342
Link to Quanjiang's session: https://chalmers.zoom.us/j/63625781640
Computer labs
The computer labs should be performed at home and will be examinated in Zoom meetings at the time slots given in the schedule.
You should submit the time slot for when you will attend the computer labs in the choodles below.
Computer lab 1: https://choodle.portal.chalmers.se/m5uopZC5vdIivSWM
Computer lab 2: https://choodle.portal.chalmers.se/b6ly8yrBSHYAaUW4
Teachers
Emil Gustavsson
Lecturer and course responsible
Business area leader within Machine Learning, Data Science, Optimization
Fraunhofer-Chalmers Centre
Email: emil.gustavsson@fcc.chalmers.se
Ann-Brith Strömberg
Examiner
Professor of mathematical optimization, Mathematical Sciences
Email: anstr@chalmers.se, Tel: 772 5378, Room: L2087
Quanjiang Yu
Exercise assistant
Ph.D. student, Mathematical Sciences
Email: yuqu@chalmers.se, Tel: 772 1094, Room: L2101
Office hours: Wednesday 9:00 - 10:00 Thursday 9:00-10:00 at https://chalmers.zoom.us/j/64492806438
Edvin Åblad
Exercise assistant
Ph.D. student, Mathematical Sciences and Fraunhofer-Chalmers Centre
Email: edvin.ablad@chalmers.se
Office hours: Tuesday 13:00 - 14:00, Friday 10:00 - 11:00 at https://chalmers.zoom.us/j/63225422882
Course literature
An Introduction to Continuous Optimization, 3rd Edition
N. Andréasson, A. Evgrafov, E. Gustavsson, Z. Nedělková, M. Patriksson, K.C. Sou, and M. Önnheim
Published by Studentlitteratur 2016 and found in the Cremona book store
Program
Lectures
The program is preliminary. Chapter numbers refer to the course book
Lecture | Date | Chapter | Content | Videos |
---|---|---|---|---|
- | 1/9 | Intro to course, administrative stuff | ||
1 | 1/9 | 1-2 | Course presentation, introduction to optimization, notations, classification | |
2 | 7/9 | 3 | Convex sets, convex functions, convex problems | |
3 | 8/9 | 4 | Introduction to optimality conditions | |
4 | 14/9 | 11 | Unconstrained optimization algorithms | |
5 | 15/9 | 5.1-5.4 | Optimality conditions | |
6 | 21/9 | 5.5-5.9 | Optimality conditions | |
7 | 22/9 | 6 | Lagrangian duality | |
8 | 28/9 | 7-8 | Introduction to linear programming | |
9 | 29/9 | 9 | Linear programming | |
10 | 5/10 | 10 | Linear programming duality | |
11 | 6/10 | 3, 4.4, 6.4 | Convex optimization | |
12 | 12/10 | --- | Integer programming | |
13 | 13/10 | 12 | Feasible direction methods | |
19/10 | 13 | Constrained optimization | ||
15 | 20/10 | --- | Summary of the course |
Exercises
Exercises numbered EX.Y can be found in the exercise sets (can be downloaded below under "Files"). 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.
There are four sessions, two in paralell, for each exercise class, you should participate in max one of these.
Exercise | Date | Assignment exercises | Exercises | Teacher exercises |
---|---|---|---|---|
1 | 4/9 | E1.2, E1.6-E1.9, 1.1, 1.2, 1.4 | E1.1, E1.4, 1.3 | |
2 | 7/9, 8/9 |
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 | 10/9, 11/9 | 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 | 14/9, 15/9 | 11.3, 11.6, 11.9, 11.11, 11.13 | 4.13, 11.5, 11.7, 11.4 | |
5 |
17/9, 18/9 |
E2.5, E2.7, E2.8, 11.2 | 5.2, E3.3 | |
6 | 21/9, 22/9 |
5.1, 5.3--5.10, 5.12, E3.1, E3.2, E3.4, E3.6 | 5.11, E3.7, 6.4, 6.10 | |
7 | 24/9, 25/9 | E3.5, E3.9, E3.10, E3.11 | E3.8, 6.1--6.3, 6.5--6.9, 6.11--6.12 | 8.1, E4.2 |
8 | 28/9, 29/9 |
8.2--8.5, 8.7, E4.1, E4.4 | 8.6, 9.1, 9.4 | |
9 | 1/10, 2/10 | E4.3, E4.5, E4.7, E4.12 | 9.2--9.3, 9.5--9.6, E4.6, E4.8--E4.11 | E5.1, E5.2, 10.13 |
10 | 5/10, 6/10 |
10.1-10.12,10.14-10.17, E5.4, E5.6, E5.8 | E5.9, E5.13 | |
11 | 8/10, 9/10 | E5.3, E5.5, E5.7, E5.11 | E5.10, E5.12, Section 6.4.2 in the course book | 12.4 |
12 | 12/10, 13/10 |
12.1--12.3, 12.5--12.14 | E6.4, 13.3, 13.5 | |
13 | 15/10, 16/10 | E6.1, E6.2, E6.5, E6.6 | 13.1--13.4, 13.6--13.8 | |
14 | 19/10, 20/10 |
Old exam | ||
15 | 22/10, 23/10 | QA |
Computer labs
Students are supposed to attend one of the sessions for each computer exercise.
Lab | Date | Content |
---|---|---|
1 | 17/9 | Steepest descent, Newton's method |
1 | 24/9 | Steepest descent, Newton's method |
AMPL | 1/10 | Students test AMPL and can ask teachers for help |
2 | 8/10 | Penalty methods, KKT condition |
2 | 15/10 | Penalty methods, KKT condition |
Assignment exercises
On Wednesdays you need to submit which questions you have solved, do this under the corresponding assignment here in canvas.
You will then need to be present in on of the sessions on either Thursday or Friday. A presenter is then chosen at random to show their solution during these sessions. It is important that you attend to exactly one of these sessions if you have made the assignment submission in Canvas.
There will be in total 24 assignment exercises.
- 20 marks implies 2 bonus points on the exam
- 12 marks implies 1 bonus point on the exam
Project
How to create groups: Create project group
Project part 1:
The aim of this part is to introduce you to mathematical modelling. The Deadline for handing in the report is 25/9 and it should be done through Canvas.
Project part 2:
The aim of this part is to introduce you to AMPL. Deadline for handing in the report is 9/10 and it should be done through Canvas.Handing in:
The model assignment is handed in through Canvas in pdf format only!
More information regarding how to hand in the report will be posted soon...
No more than three 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.
Language:
English
Writing tools:
Prefarably Latex but other word formatting tools are also ok (such as word, etc) as long as the report is readable as pdf.
Student representatives and course evaluation
Useful information about the course evaluation process and your role in the same (Links to an external site.) is found on the Student portal.
Information about being a student representative.
The student representatives for the course are:
Ahmed Groshar ahgroshar@gmail.com
Sana Hamdi sana.hmd@outlook.com
Sanna Persson sanna.persson@live.com
Alexander Rodin rodina@student.chalmers.se
Jesper Strömberg jesstr@student.chalmers.se
- The mid-term course evaluation meeting will take place on Friday, September 25, at 13–14
- Questions to address during the meeting should be conveyed via the student representatives
- Published notes from the meeting
Examination
The schedule for exams at MV is found here. Note that this page concerns the GU-version of the course, so instructions about registration for the exam may be different for Chalmers students. The exam and the hours are the same, though.
Dates for exams at Chalmers is found on this link.
Old exams
tentalosning_TMA947_201029.pdf
tentalosning_TMA947_200818.pdf
tentalosning_TMA947_191031.pdf
tentalosning_TMA947_181101.pdf
tentalosning_TMA947_180821.pdf
tentalosning_TMA947_180405.pdf
tentalosning_TMA947_180109.pdf
tentalosning_TMA947_170824.pdf
tentalosning_TMA947_170412.pdf
tentalosning_TMA947_170110.pdf
tentalosning_TMA947_160825.pdf
tentalosning_TMA947_160405.pdf
tentalosnins_TMA947_160112.pdf
tentalosning_TMA947_150827.pdf
tentalosning_TMA947_150414.pdf
tentalosning_TMA947_150113.pdf
tentalosning_TMA947_140422.pdf
tentalosning_TMA947_131217.pdf
tentalosning_TMA947_130829.pdf
tentalosning_TMA947_121217.pdf
tentalosning_TMA947_120410.pdf
tentalosning_TMA947_111212.pdf
tentalosning_TMA947_110426.pdf
tentalosning_TMA947_101213.pdf
tentalosning_TMA947_100406.pdf
tentalosning_TMA947_091214.pdf
tentalosning_TMA947_090827.pdf
tentalosning_TMA947_090414.pdf
tentalosning_TMA947_081215.pdf
tentalosning_TMA947_080828.pdf
tentalosning_TMA947_080325.pdf
tentalosning_TMA947_071217.pdf
Files
Misc:
- 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)
- Index (3rd Edition)
- AMPL intro
Lecture notes:
Exercise sets
- Exercise set 1
- Exercise set 2
- Exercise set 3
- Exercise set 4
- Exercise set 5
- Exercise set 6
Computer labs
- Computer exercise 1, PM
- Computer exercise 1, files
- Computer exercise 2, PM
- Computer exercise 2, files
Project
- Project part 1, PM
- Introduction to AMPL
AMPL Installation
Course summary:
Date | Details | Due |
---|---|---|
|