Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Glineur François;
Language
English
Prerequisites
A basic optimization course (such as LINMA1702) and basic knowledge in real analysis and linear algebra (such as provided by FSAB1101 and FSAB1102)
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 : | |
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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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The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
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
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
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
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Data Science Engineering
Master [120] in Biomedical Engineering
Master [120] in Mathematics
Master [120] in Computer Science and Engineering
Master [120] in Mathematical Engineering
Master [120] in Statistic: General
Master [120] in Computer Science
Master [120] in Data Science: Information Technology