 | |
| MATH0461-1 | Introduction to numerical optimization
 |
|
| Duration : | 30h Th, 30h Pr |
|
| Credits/ECTS : |
| Master in Electrical Engineering, in-depth approach, 1st year | | Second semester | | 5 |
|
| Master in Electro-mechanical Engineering, Teaching Focus, 2nd year | | Second semester | | 5 |
|
| Master in Computer Engineering, in-depth approach, 1st year | | Second semester | | 5 |
|
| Master in Computer science, Research Focus, 2nd year | | Second semester | | 6 |
|
| Master in Mechanical Engineering, in-depth approach, 1st year | | Toute l'année | | 5 |
|
| Master in Engineering Physics, in-depth approach, 1st year | | Second semester | | 5 |
|
| Master in Engineering Physics, in-depth approach, 2nd year | | Second semester | | 5 |
|
| Master en ingénieur civil électricien, à finalité spécialisée en technologies durables en automobile, 1st year | | Second semester | | 5 |
|
| Master in Electrical Engineering, specialized approach, 1st year | | Second semester | | 5 |
|
| Master in Computer Engineering, specialized approach, 1st year | | Second semester | | 5 |
|
| Master ingénieur civil mécanicien, à finalité spécialisée en technologies durables en automobiles, 1st year | | Toute l'année | | 5 |
|
| Master in Mechanical Engineering, specialized approach, 1st year | | Toute l'année | | 5 |
|
| Master in Engineering Physics, specialized approach, 1st year | | Second semester | | 5 |
|
| Master in Engineering Physics, specialized approach, 2nd year | | Second semester | | 5 |
|
| Master in Computer science | | Toute l'année | | 6 |
|
| Master in Mathematical Sciences, professional focus in computer science, 2nd year | | Toute l'année | | 6 |
|
|
|
| Holder(s) : | Quentin Louveaux |
|
| Language : | English language |
|
| Course 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 mostly problems where all the involved functions are linear leading to so-called linear programs. We will first focus on modeling as many problems as possible as linear programs. We will also study the different existing techniques to solve such linear programs as well as analyzing the nice properties of these problems. The second part of the course is devoted to nonlinear problems and in particular to conic problems that keep the nice properties of linear programs.
This course is given in English. The textbook is however in French. |
|
| Course objective : | The following concepts are studied in the course:
- Modeling by means of a linear program
- Convexity and geometry of linear programs
- The 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
- Introduction to integer programming |
|
| Prerequisites : | Basic course in linear algebra |
|
| Workshops : | 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. |
|
| Written notes : | D. Bertsimas, J. Tsistsiklis. Introduction to linear optimization, Dynamic Ideas, 1997. |
|
| Assessment : | 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%. |
|
| Remarks : | The course is taught in English. |
|
|
| |
