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| MATH0461-2 | Introduction to numerical optimization
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| Duration : | 30h Th, 20h Pr, 25h Proj. |
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| Number of credits : |
| Master in Biomedical Engineering, research focus, 1st year | | 5 |
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| Master in Electrical Engineering, research focus, 1st year | | 5 |
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| Master in Electro-mechanical Engineering, research focus, 2nd year | | 5 |
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| Master of science in computer science and engineering, research focus, 2nd year | | 5 |
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| Master in Computer science, Research Focus, 2nd year | | 5 |
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| Master in Engineering Physics, research focus, 1st year | | 6 |
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| Master in Engineering Physics, research focus, 1st year | | 5 |
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| Master in Engineering Physics, research focus, 2nd year | | 5 |
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| Master in in Electrical Engineering, professional focus in sustainable car technologies, 1st year | | 5 |
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| Master in Electrical Engineering, specialized approach, 1st year | | 5 |
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| Master in Engineering Physics, specialized approach, 1st year | | 6 |
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| Master in Engineering Physics, specialized approach, 1st year | | 5 |
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| Master in Engineering Physics, specialized approach, 2nd year | | 5 |
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| Lecturer : | Quentin Louveaux |
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Language(s) of instruction :
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| English language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| 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. |
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Learning outcomes of the course :
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| 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)
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Basic course in linear algebra and calculus. |
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Planned learning activities and teaching methods :
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| Traditional tutorials are organized for roughly 20 hours.
A larger project consisting in modeling and solving a real-world problem using a linear programming package is also organized. An optional project of implementation of a nonlinear method can be realized. |
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Mode of delivery (face-to-face ; distance-learning) :
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| face-to-face |
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Recommended or required readings :
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| D. Bertsimas, J. Tsistsiklis. Introduction to linear optimization, Dynamic Ideas, 1997.
M. Bierlaire. Introduction à l'optimisation différentiable. Presses polytechniques et universitaires romandes. 2006 |
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Assessment methods and criteria :
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| The exam is oral and counts for 75% of the final grade. The modeling project counts for 25%. The optional project may provide a bonus for the student of 0 to 3 points to the final grade (/20). |
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Work placement(s) :
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Organizational remarks :
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| The course is taught in English. |
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Contacts :
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