Due to the COVID-19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Glineur François;
Language
English
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.
Aims
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 ; trust-region methods ; 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 ; trust-region methods ; 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
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
The course is comprised of lectures, exercise sessions and computer labs, as well as a series of homeworks to be carried out in small groups.
Evaluation methods
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
Students will be evaluated with an individual written exam, based on the above-mentioned objectives. Students also carry out a series of homeworks in small groups, which are taken into account for the final grade.
Online resources
Course documents (notes, slides, exercises and homeworks) are available on Moodle : https://moodleucl.uclouvain.be/course/view.php?id=8194
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.
- Trust-region methods, A. Andrew R. Conn, Nicholas I. M. Gould, Ph. Philippe L. Toint, SIAM, 2000.
- Lectures on Convex Optimization, Y. Nesterov, Springer, 2018
Faculty or entity
MAP
Force majeure
Evaluation methods
Unless only remote evaluations are allowed by the sanitary rules, the written exam is organized on site. Students unable to participate, as attested by a medical quarantine certificate, will be offered the opportunity to take the exam remotely at the same time. This parallel examination, written and proctored, will be of the same type and will cover the same topics as the main examination.
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Aims
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
Master [120] in Biomedical Engineering