
M2 Optimization 

``Stochastic Optimization'' 
Professors
The course was given for several years in the
M2 Optimization
as an introductory course to stochastic optimization.
Goals
The course presents both theoretical and numerical aspects of decision problems
with uncertainty, where one sets a probabilistic framework in order to minimize
the expectation of a cost. Two directions are explored:

we investigate the socalled "openloop" situation, that is,
the case where decisions do not depend on information available for the problem,
and we thoroughly study the stochastic gradient method and its variants,

we also study "closedloop" optimization problems, that is, the case where
decisions are based on partial information (often corresponding to measurements
made in the past when facing an unknown future).
Such problems are of course wellmotivated by decision problems in the industry.
They also have a deep mathematical content, especially in the dynamic case when
only the past information is available. In this setting the decision is a function
in a high dimensional space and therefore the numerical aspects also are challenging.
Structure

Lesson 1

Issues in decision making under uncertainty
(P. Carpentier).
Slides

Convex analysis and probability tools for stochastic optimization  Part I
(V. Leclère).
Slides

Lesson 2

Stochastic gradient method overview
(P. Carpentier).
Slides

Convex analysis and probability tools for stochastic optimization  Part II
(V. Leclère).
Slides

Lesson 3

Generalized stochastic gradient method
(P. Carpentier).
Slides

Stochastic Programming. The twostage case
(V. Leclère).
Slides

Lesson 4

Bellman operators and Stochastic Dynamic Programming
(V. Leclère).
Slides

Applications of the stochastic gradient method
(P. Carpentier).
Slides

Lesson 5

Discretization issues of general stochastic optimization problems
(P. Carpentier).
Slides

Scenario decomposition: LShaped and Progressive Hedging methods
(V. Leclère).
Slides

Lesson 6

The Stochastic Dual Dynamic Programming (SDDP) approach
(V. Leclère).
Slides

Decomposition approaches for large scale stochastic optimization problems
(P. Carpentier).
Slides

Evaluation

Articles presentation
(P. Carpentier).

Written exam
(V. Leclère).
Course resources
External resources
Page managed by P. Carpentier
(last update: July 06, 2021)