ENSTA ParisTech - Université Paris 1 Panthéon-Sorbonne
Master MMMEF - Track "Optimization, control and operations research"
Academic year 2014/2015
"Stochastic Optimisation: Numerical Methods"
The aim of this course is to provide a framework for extending the optimization methodology already studied in the convex deterministic case to the stochastic case, both from the theoretical and the numerical points of view.
The course consists of two parts:
During the first part of the course, we put the focus on large-scale optimization problems and decomposition/coordination methods.
- we are first interested in stochastic open-loop optimization problems, and we thoroughly study the stochastic gradient method and its variants,,
- we then move to closed-loop optimization problems, and study on the one hand the significance of the information structure for such problems, and on the other hand the difficulties related to the discretization of these problems.
The course takes place on Tuesday afternoon from 14:00 to 17.30 at ENSTA
(Getting to ENSTA),
and is given in English.
Lesson 1 (January 13, room 2.4.30)
Introduction to Stochastic Optimization: motivations and objectives
of the course, reminders from the deterministic case and transition
to the stochastic case. Overview of the stochastic gradient method.
Lesson 2 (January 20, room 2.4.30)
Generalized stochastic gradient method: introduction to the Auxiliary
Problem Principle, convergence in the cases without and with constraints.
Lesson 3 (February 3, room 2.4.12)
Exercises on the stochastic gradient method and presentation of extensions
of the method to the case of constraint in expectation and in probability.
Lesson 4 (February 10, room 2.4.12)
Dual effect in stochastic optimization: information structure, dual
effect issues and application in stochastic optimal control.
Lesson 5 (February 17, room 2.4.12)
Discretization: issues of discretization in stochastic optimization,
counterexample, convergence theorem.
Lesson 6 (March 3, room 2.4.30).
Course notes about stochastic optimization (in English)
Course notes about the stochastic gradient method (in French)
Toolbox ''Stochastic Gradient''(in French)
Le but de cette boîte à outils (écrite en langage Scilab) est d'illustrer sur un exemple simple le comportement du gradient stochastique ainsi que sa vitesse de convergence, et de montrer ce qu'apporte la technique de moyennisation.
Page managed by P. Carpentier
(last update: February 18, 2015)