
University ParisSaclay 

Master ``Optimization'' 
Academic Year 2018/2019 
First term's advanced courses 
Stochastic Optimization 
Professors
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.
This course is part of the M2 Optimization program (ParisSaclay University).
Structure
The course takes place at ENSTA on Wednesday, from 09:00 to 12:00 and from 14:00 to 16:00,
and is given in English.
Getting to ENSTA

Lesson 1 (November 21, room 2.2.36)

09:00  12:00 (P. Carpentier)
Issues in decision making under uncertainty.
Slides

14:00  16:00 (V. Leclère)
Convex analysis and probability tools for stochastic optimization  Part I.

Lesson 2 (November 28, room 2.2.36)

09:00  12:00 (P. Carpentier)
Stochastic gradient method overview.
Slides

14:00  16:00 (V. Leclère)
Convex analysis and probability tools for stochastic optimization  Part II.

Lesson 3 (December 05, room 2.2.36)

09:00  12:00 (P. Carpentier)
Generalized stochastic gradient method.
Slides

14:00  16:00 (V. Leclère)
Stochastic Programming. The twostage case.

Lesson 4 (December 12, room 2.2.36)

09:00  12:00 (V. Leclère)
Scenario decomposition: LShaped and Progressive Hedging methods.

14:00  16:00 (P. Carpentier)
Stochastic gradient method with constraint in expectation and applications.
Slides

Lesson 5 (December 19, room 2.2.36)

09:00  12:00 (P. Carpentier)
Discretization issues of general stochastic optimization problems.
Slides

14:00  16:00 (V. Leclère)
Bellman operators and Stochastic Dynamic Programming.

Lesson 6 (January 09, room 2.2.36)

09:00  12:00 (V. Leclère)
The Stochastic Dual Dynamic Programming (SDDP) approach.

14:00  16:00 (P. Carpentier)
Decomposition approaches for large scale stochastic optimization problems.
Slides

Evaluation (January 16, room 2.2.36).

09:00  12:00 (P. Carpentier)
Articles presentation  Session 1.

14:00  16:00 (V. Leclère)
Written exam.

Evaluation (January 21, room 2.2.36).

09:00  12:00 (P. Carpentier)
Articles presentation  Session 2.
Course resources
External resources
Page managed by P. Carpentier
(last update: June 23, 2018)