Data Driven Robust Optimization
Description
This is a master level course given at École des Ponts Paristech as part of the Master of Applied Mathematics of the school.
Uncertainty in optimization can be difficult to deal with. In this course we consider a constraint of the form $f(u,x) \leq 0$ where u is uncertain. Two approaches are possible here :
- Stochastic Programming approach : we assume that $u$ is a random variable with known law, and reformulate the constraint as $\mathbb{P}(f(u,x) \leq 0) \geq 1 - \varepsilon$.
- Robust Optimization approach : we assume that $u$ is an element of un uncertainty set $U$ and want the constraint to be satisfied for all $u\in U$.
In both cases it is sometimes difficult to model uncertainty, either by defining its law or its uncertainty set. The course will show how to leverage the availability of data (realization of the uncertain
parameter $u$) to construct a smart uncertainty set $U$ that is both tractable and offering good robustness guarantees.
Pre-requisite
- Convex analysis
- Linear and convex optimization
- Statistical test
Planning
- Monday 03/02, 8h30-11h30, P315, Introduction to robust optimization
- Monday 10/02, 8h30-11h30, P315, Sample approach to chance constraint
- Monday 17/02, 8h30-11h30, P315, Reformulating non-linear robust constraints
- Monday 24/02, 8h30-11h30, P315, Data Driven Robust Optimization method
- Monday 02/03, 8h30-11h30, P315, Statistical tools
- Monday 09/03, 8h30-11h30, P315, Data Driven Uncertainty Set : discrete case
- Monday 16/03, 8h30-11h30, P315, Data Driven Uncertainty Set : continuous case
- Monday 23/03, 8h30-11h30, P315, Exam
Handrwitten notes
File with the handwritten notes
2021 Exam
Answer to be sent by email for tuesday 23 8am
Past Exam
Main references
More references