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| MATH0461-1 | Introduction to numerical optimization
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
| Master in Electrical Engineering, in-depth approach, 1st year | | Second semester | | 5 |
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| Master in Electro-mechanical Engineering, Teaching Focus, 2nd year | | Second semester | | 5 |
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| Master in Computer science, Research Focus, 2nd year | | Second semester | | 6 |
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| Master in Mechanical Engineering, in-depth approach, 2nd year | | Toute l'année | | 5 |
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| Master in Engineering Physics, in-depth approach, 1st year | | Second semester | | 5 |
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| Master in Engineering Physics, in-depth approach, 2nd year | | Second semester | | 5 |
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| Master en ingénieur civil électricien, à finalité spécialisée en technologies durables en automobile, 1st year | | Second semester | | 5 |
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| Master in Electrical Engineering, specialized approach, 1st year | | Second semester | | 5 |
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| Master in Engineering Physics, specialized approach, 1st year | | Second semester | | 5 |
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| Master in Engineering Physics, specialized approach, 2nd year | | Second semester | | 5 |
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| Master in Mathematical Sciences, professional focus in computer science, 2nd year | | Second semester | | 6 |
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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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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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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 consists only of exercises. Every material is allowed for consulting during the exam. The exam counts for 75% of the final grade. The modeling project counts for 25%. The optional project counts for 25% and replaces one question of the exam. |
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Organizational remarks :
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| The course is taught in English. |
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