Beniamin BOGOSEL

MAP435 Optimization and Control (2020-present) This course takes place in the second year of the Polytechnique Engineer programme. The course is related to optimization and optimal control aspects and is done by Grégoire Allaire. I am responsible for doing the practical sessions for two groups of students (exercises, numerical algorithms).

Computational Maths 2: Numerical Optimization (2018-present)

This course takes place in the second year of the Bachelor program at Ecole Polytechnique. It deals with optimization problems with an emphasis on numerical algorithms.

Course Materials:

• Optimization in dimension one: Courses 1-2
  • Python Notebook illustrating the trisection method: Trisection
  • Python Notebook: Newton method
  • Python Notebook: Line-search
• Optimization in higher dimensions (Gradient Descent, Newton): Courses 3-4
  • Python Notebook: Gradient Descent
  • Python Notebook: Ill conditioned case
  • Python Notebook: Newton method
• Optimization in higher dimensions (quasi-Newton, Conjugate Gradient,...): Course 5
  • Python Notebook: Scipy Minimize Example
• Optimization under constraints (theory of Lagrange multipliers, intro to Linear Programming): Courses 6-7
  • Python Notebook: Example using scipy.linprog
  • Python Notebook: Optimal Assignment Problem
  • Matlab code: Solving Sudoku with LP sudokuLP.m

Practical Sessions:

• Session 1
• Session 2
• Session 3
• Session 4
• Session 5
• Session 6

Modal MAP472A Modelization and practical aspects related to applied mathematics. Students work in groups on subjects involving models and numerical simulations. Subjects I proposed were related to: high order Runge-Kutta methods implemented using Butcher tables, modelization and simulation of a double pendulum, inverted cart pendulum, the $n$-body problem.

Optimal design of structures - MAP562 (2018-present) by Grégoire Allaire. For more details regarding the course take a look at this old page of the course: link. Students which are enrolled have access to all materials regarding the course on the Moodle platform

My responsibilities mainly deal with the exercise and coding tasks.

The course is done by Samuel Amstutz starting from the year 2020.

MAP412 Introduction à l'Analyse Numérique (2019-2020)

by Marc Massot and Laurent Séries. This course replaced MAP411. I was responsible with teaching and finding problems and exercises for the practical sessions together with Maxime Breden and Teddy Pichard.

Introduction - Optimisation de formes (ENSTA) 2018

Documents de cours (dernière mise à jour: 09/12/2018)

Cours 1 (03/12/2018): slides, notes TP

• Codes FreeFem - Introduction : codes

Cours 2 (10/12/2018): slides, notes TP2

• Codes FreeFem - Comparaison avec ou sans materiau ersatz : codes
• Codes FreeFem - Exemple d'optimisation paramétrique : codes
• Codes FreeFem - Exemple d'optimisation geometrique : codes
• Codes FreeFem - Exemple d'optimisation avec Level-Set : codes

Cours 3 (01/02/2019): slides session pratique

• Codes FreeFem - Simulation Navier-Stokes : codes
• Useful reference on shape optimization using the Navier-Stokes equations: link

Liste de références (non exhaustive) : RefList.pdf

Merci Charles Dapogny. Voir son cours en suivant ce lien
Merci Grégoire Allaire. Voir son cours en suivant ce lien

MAP411 Approximation numerique et optimisation 2018

Questions concernant le TD et les exos : beniamin.bogosel_at_cmap.polytechnique.fr

Voir le detail du cours sur Moodle

Corrections :

PC1 : voir Moodle

PC2 : voir pdf, voir aussi Moodle

PC3 : voir Moodle

PC4-5-6 : correction partielle des exos 4 et 5 : ici

PC7-8 : voir Moodle

PC8-9 : voir Moodle pour Exercices 1 et 2. Le reste dans le document suivant : Correction8_9

PC10 : correction partielle des exercices 2 et 3 dans le document suivant : Correction10

Un document contenant des idées utilisées dans la résolution des exos : doc