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
Q2
Teacher(s)
Nesterov Yurii;
Language
English
Prerequisites
Basic knowledge of Nonlinear Analysis and Linear Algebra.
The target audience is the students interested in scientific computing, machine learning and optimization in engineering.
The target audience is the students interested in scientific computing, machine learning and optimization in engineering.
Main themes
- General nonlinear optimization.
- Smooth and non-smooth convex optimization.
- Interior-point methods.
Aims
At the end of this learning unit, the student is able to : | |
| 1 |
Learning outcomes:
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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
- General problem of nonlinear optimization. Black-box concept. Iterative methods and analytical complexity. Gradient method and Newton method. Local complexity analysis.
- Convex optimization: convex sets and functions; minimization of differentiable and non-differentiable convex functions; lower complexity bounds; optimal methods.
- Interior-point methods: notion of self-concordant functions and barriers; path-following methods; structural optimization.
Teaching methods
The course is given in 12-15 lectures. The computer projects are implemented by the students themselves with supporting consultations.
Evaluation methods
In the written exam (in English or French) there are four questions, one for each chapter of the course (up to 5 points for each question). The marks for the exam and the exercises are combined in the final mark.
Online resources
The full syllabus (in English) can be downloaded from the web page of the course.
Bibliography
- Yu.Nesterov. "Introductory lectures on convex optimization. Basic course", Kluwer 2004
- P. Polyak, « Introduction in optimization », J. Willey & Sons, 1989
- Yu. Nesterov, A. Nemirovsky, « Interior-point polynomial algorithms in nonlinear optimization », SIAM, Philadelphia, 1994.
Faculty or entity
MAP
