5.00 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Glineur François; Nunes Grapiglia Geovani;
Language
English
> French-friendly
> French-friendly
Prerequisites
A basic optimization course (such as LINMA1702) and basic knowledge in real analysis and linear algebra (such as provided by LEPL1101 and LEPL1102)
Main themes
Linear optimization, convex optimization (including structured conic optimization) ; duality and applications ; interior-point methods ; first-order methods ; trust-region methods ; use of a modeling language.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 |
Learning outcomes: AA1.1, AA1.2, AA1.3 AA2.1, AA2.2, AA2.4, AA2.5 AA5.3, AA5.5 More specifically, at the end of the course the student will be able to :
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Content
Models: Advanced modeling techniques for linear and convex optimization ; structured conic optimization ; convex duality with applications (alternatives, sensitivity analysis and robust optimization) ; Lagrangian duality
Methods: path-following interior-point methods for convex optimization (self-concordant barriers) ; first-order methods for convex and non-convex optimization (including stochastic methods) ; algorithmic complexity and convergence rates ; introduction to the AMPL modeling language.
Applications in various domains, such as data analysis, machine learning, finance, shape or structural optimization (mechanics), telecommunications, etc.
Methods: path-following interior-point methods for convex optimization (self-concordant barriers) ; first-order methods for convex and non-convex optimization (including stochastic methods) ; algorithmic complexity and convergence rates ; introduction to the AMPL modeling language.
Applications in various domains, such as data analysis, machine learning, finance, shape or structural optimization (mechanics), telecommunications, etc.
Teaching methods
The course is comprised of lectures, exercise sessions and computer labs, as well as a series of homework assignments to be carried out in small groups.
Evaluation methods
Students are assessed individually with a written exam organized during the session, based on the learning outcomes listed above. In addition, students complete a series of homework assignments in small groups during the first term. The grade of the homework is acquired for all the sessions of the academic year (it is not possible to redo the homework assignments in the second session).
The final grade is awarded on the basis of the homework assignments (8 points out of 20) and the exam (12 points out of 20).
The final grade is awarded on the basis of the homework assignments (8 points out of 20) and the exam (12 points out of 20).
Online resources
Bibliography
- Convex Optimization, Stephen Boyd et Lieven Vandenberghe, Cambridge University Press, 2004.
- Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, Aharon Ben-Tal, Arkadi Nemirovski, SIAM 2001.
- Interior point methods for linear optimization, Cornelis Roos, Tamas Terlaky, Jean-Philippe Vial, Springer, 2006.
- Introductory Lectures on Convex Optimization: A Basic Course, Yurii Nesterov, Kluwer, 2004.
- Lectures on Convex Optimization, Y. Nesterov, Springer, 2018
Teaching materials
- Exercises and labs booklet provided on Moodle
- Compilation of previous examens provided sur Moodle
Faculty or entity
MAP
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Biomedical Engineering
Master [120] in Mathematics
Master [120] in Computer Science and Engineering
Master [120] in Computer Science
Master [120] in Mathematical Engineering
Master [120] in Data Science Engineering
Master [120] in Data Science: Information Technology