TMA947/MMG621 Nonlinear optimisation
Exam review
The exam review will be held on Thursday 28/11 at 12.00 in MVL13.
There you can collect your exam and ask questions regarding the corrections.
Exam and solutions
tentalosning_TMA947_191031.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.
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
Michael Patriksson
Examiner
Professor of applied mathematics, Mathematical Sciences
Email: mipat@chalmers.se, Tel: 772 5329, Room: L2084
Quanjiang Yu
Exercise assistant
Ph.D. student, Mathematical Sciences
Email: yuqu@chalmers.se, Tel: 772 1094, Room: L2101
Edvin Åblad
Exercise assistant
Ph.D. student, Mathematical Sciences and Fraunhofer-Chalmers Centre
Email: edvin.ablad@chalmers.se
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
Program
The schedule of the course is in TimeEdit.
Lectures
The program is preliminary. Chapter numbers refer to the course book
| Lecture | Date | Chapter | Content |
|---|---|---|---|
| 1 | 3/9 | 1-2 | Course presentation, introduction to optimization, notations, classification |
| 2 | 9/9 | 3 | Convex sets, convex functions, convex problems |
| 3 | 10/9 | 4 | Introduction to optimality conditions |
| 4 | 16/9 | 11 | Unconstrained optimization algorithms |
| 5 | 17/9 | 5.1-5.4 | Optimality conditions |
| 6 | 23/9 | 5.5-5.9 | Optimality conditions |
| 7 | 24/9 | 6 | Lagrangian duality |
| 8 | 1/10 | 7-8 | Introduction to linear programming |
| 9 | 2/10 | 9 | Linear programming |
| 10 | 7/10 | 10 | Linear programming duality |
| 11 | 8/10 | 3, 4.4, 6.4 | Convex optimization |
| 12 | 14/10 | --- | Integer programming |
| 13 | 15/10 | 12 | Feasible direction methods |
| 21/10 | 13 | Constrained optimization | |
| 15 | 22/10 | --- | 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.
| Exercise | Date | Assignment exercises | Exercises | Teacher exercises |
|---|---|---|---|---|
| 1 | 6/9 | E1.2, E1.6-E1.9, 1.1, 1.2, 1.4 | E1.1, E1.4, 1.3 | |
| 2 | 9/9 | 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 | 13/9 | 4.2, 4.3, 4.4, 4.5, 4.12, 4.15, 4.16 | 4.1, 4.4b, 4.6, 4.13 | |
| 4 | 16/9 | E1.3, E1.5, E1.10, E1.11 | 11.3, 11.6, 11.9, 11.11, 11.13 | 11.5, 11.7, 11.4 |
| 5 |
20/9 |
|||
| 6 | 23/9 | 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 |
| 7 | 27/9 | E3.8, 6.1--6.3, 6.5--6.9, 6.11--6.12 | 5.11, E3.7, 6.4, 6.10 | |
| 8 | 30/9 | E3.5, E3.9, E3.10, E3.11 | 8.2--8.5, 8.7, E4.1, E4.4 | 8.1, E4.2 |
| 9 | 4/10 | 9.2--9.3, 9.5--9.6, E4.6, E4.8--E4.11 | 8.6, 9.1, 9.4 | |
| 10 | 7/10 | 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 |
| 11 | 11/10 | E5.10, E5.12, Section 6.4.2 in the course book | E5.9, E5.13 | |
| 12 | 14/10 | E5.3, E5.5, E5.7, E5.11 | 12.1--12.3, 12.5--12.14 | 12.4, E6.4 |
| 13 | 18/10 | 13.1--13.4, 13.6--13.8 | 13.3, 13.5 | |
| 14 | 21/10 | E6.1, E6.2, E6.5, E6.6 | ||
| 15 | 25/10 | Old exam |
Computer labs
Students are supposed to attend one of the sessions for each computer exercise.
Please choose one time slot for Computer lab 1 at the following link:
https://choodle.portal.chalmers.se/X62SwbiWXggvJ5Sg
Please choose one time slot for Computer lab 2 at the following link:
https://choodle.portal.chalmers.se/dI6qfP82VOR8orAC
| Lab | Date | Content |
|---|---|---|
| 1 | 19/9 | Steepest descent, Newton's method |
| 1 | 26/9 | Steepest descent, Newton's method |
| AMPL | 3/10 | Students test AMPL and can ask teachers for help |
| 2 | 10/10 | Penalty methods, KKT condition |
| 2 | 17/10 | Penalty methods, KKT condition |
Assignment 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.
- 20 marks implies 2 bonus points on the exam
- 12 marks implies 1 bonus point on the exam
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
Project part 1:
The aim of this part is to introduce you to mathematical modelling. The Deadline for handing in the report is 27/9 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 11/10 and it should be done through Canvas.
An introduction to AMPL can be found here.
The necessary AMPL-files are: Belgium.mod, Belgium.dat, and Belgium.run.
Handing in:
The model assignment is handed in through Canvasin pdf format only!
More information regarding how to hand in the report will be posted soon...
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.
Language:
English
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:
| Maitreya Deepak Dave | maitreya@student.chalmers.se |
| David Larsson | lardavi@student.chalmers.se |
| Sebastian Oleszko | oleszko@student.chalmers.se |
| Julia Szulc | juliasz@student.chalmers.se |
| Mattias Torstensson | mattors@student.chalmers.se |
Examination
Old exams
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
Lectures:
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- lecture13.pdf
-lecture14.pdf
-course_summary.pdfcourse_summary.pdf
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
For ampl-mswin64: https://send.firefox.com/download/1778d99be39a0b21/#CwMmqzTDWlUO-cmjsyMv8Q
For ampl-linux-intel64: https://send.firefox.com/download/6185fed2aa5f2f4d/#SWe3u8BSGgdN8O5EBH9dsQ
Course summary:
| Date | Details | Due |
|---|---|---|