Duration
30h Th, 20h Pr, 25h Proj.
Number of credits
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
In a large number of engineering problems, many decisions can be undertaken leading to different solutions, some of them being more interesting than others. A way to decide on the best decision is to come up with a mathematical model in which all decisions are variables and the choice is made by considering a function of the values of all variables.
This formalism modeling many real-life problems is called mathematical programming. In a mathematical program, we define a set of decision variables, constraints linking the variables and defining what is a feasible solution and finally an objective function to optimize. Depending on the properties of all the considered functions, the obtained optimization problem can be more or less difficult to solve. In this course we consider three types of optimization problems: linear problems and their structure (duality), nonlinear problems that keep the nice structure (conic problems) and finally problems without any structure.
The following concepts are studied in the course:
- The revised Simplex Algorithm
- Duality for linear programming
- Post-optimal analysis and the Dual Simplex Algorithm
- Introduction to interior point methods
- Optimality conditions for nonlinear programs
- Conic programming and duality
- Numerical methods for nonlinear methods
This course is given in English.
Learning outcomes of the learning unit
At the end of the course, the student will be able to
- formulate a real problem in terms of a mathematical optimization model
- determine the complexity of an optimization problem and in particular whether it can be solved in polynomial time
- write the dual of a linear or a conic problem
- apply or implement the main optimization algorithms (simplex, dual simplex, interior-point methods, gradient descent, quasi-Newton)
Prerequisite knowledge and skills
Basic course in linear algebra and calculus. Some basic knowledge of a programming language is also required.
Planned learning activities and teaching methods
Traditional tutorials are organized for roughly 20 hours. A larger project consisting in modeling and solving a real-world problem using a linear and convex programming package is also organized.
Mode of delivery (face to face, distance learning, hybrid learning)
The lecture is given in face-to-face.
There are enough seats in the room to accomodate all students with one free seat in between all students. All lectures are also podcasted.
Organisational adjustments related to the current health context
If face-to-face is allowed:
Oral exam (theory + exercises) with preparation
If remote evaluation as imposed by the health conditions:
Oral exam by videoconference without preparation
Recommended or required readings
D. Bertsimas, J. Tsistsiklis. Introduction to linear optimization, Dynamic Ideas, 1997. M. Bierlaire. Introduction à l'optimisation différentiable. Presses polytechniques et universitaires romandes. 2006
Assessment methods and criteria
Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.
The exam is oral and includes a question of theory and a question of exercises.
For the final grade, the grade of the exam counts for 2/3, and the project grade for 1/3.
If the project is not submitted in December, it has to be submitted in August (with the same statement).
No project submitted implies a "no show" grade.
Work placement(s)
Organizational remarks
The course is taught in English.
All documents are avilable on
https://dox.uliege.be/index.php/s/uv41XbH1cgFLyeC
Contacts
The professor is Quentin Louveaux q.louveaux@uliege.be
The teaching assistant is Mathias Berger mathias.berger@uliege.be