The  program will be announced in the next few days

Cours:

Cours 1:  Mounir  Haddou

Titre: Optimisation non différentiable; Quelques applications 

Durée : 10h

Nom de l'enseignant : Haddou 

Prénom de l'enseignant : Mounir

Institution de l'enseignant :  Institut National des Sciences Appliquées de Rennes  

Pays de l'enseignant : France

Objectifs, finalités :

Le but de ce cours est de donner une introduction à l’optimisation convexe non-différentiable, d’introduire plusieurs algorithmes modernes ou remis au goût du jour, reconnus pour leur efficacité pour résoudre ou approcher des problèmes rencontrés en statistiques et analyse de données. 

Contenu :

      - Convexité et non-différentiabilité.

      - Méthodes de gradients et sous-gradients accélérées.

       - Gradient stochastique et gradient contraint.

       - Méthodes proximales.

       - Méthodes d’optimisation semi-lisse.

       - Lagrangiens augmentés et méthodes ADMM (directions alternées sur les  multiplicateurs)

 Applications :

      - Estimation de matrices de covariance ( avec inverse creuse).

      - Analyse en Composantes Principales creuses ou sélectives.

      - Paramétrisation de faible rang.

      - Support Vector Machine linéaires et non linéaires.

      - Régression logistique

Cours 2: Francesco Silva Alvarez 

Titre :  Introduction to stochastic differential equations and stochastic control.

Durée : 6h

Nom de l'enseignant : Francesca  Carlotta Chittaro 

Institution de l'enseignant : Université de Toulon 

Pays de l'enseignant : France

Abstract:

In these lectures we review the some key elements in the theory of stochastic differential equations and controlled diffusion processes. We begin by recalling some basic tools from stochastic analysis such as continuous time martingales, Brownian motion and the associated stochastic integral. Next, we introduce stochastic differential equations and we provide some important results such as existence and uniqueness as well as the relations with elliptic and parabolic differential equation. Finally, in the last part of the course, we define stochastic optimal control problems and characterize the optimal cost functional, parameterized by the initial time and the initial state of the decision-maker, as the unique viscosity solution to a second order Hamilton-Jacobi-Bellman equation. 

Cours 3 : Enrique Zuazua

Titre : Control, Numerics and Machine Learning

Durée : 6h

Nom de l'enseignant : Enrique Zuazua

Institution de l'enseignant : Alexander von Humboldt-Professorship

Pays de l'enseignant : Allemagne

Abstract

After a short historical introduction, we shall present and discuss the problem of controllability of Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE) arising in various areas of Science and Technology. It consists in analyzing whether, by means of a suitable and feasible controller, the solution of a dynamical system can be driven to a desired final configuration (or close to it).

We shall also discuss its dual version, the so-called observability problem. It concerns the possibility of measuring or observing, by suitable sensors, the whole dynamics of the system through partial measurements.

We shall also address some of the problems arising in the modern theory of Machine Learning, which is strongly inspired and influenced by some of the fundamental ideas and techniques in Control Theory. An introduction to this topic will also be presented, focusing mainly on the use of control techniques for the analysis of Deep Neural Networks as a tool to address, for instance, the problem of Supervised Learning.We shall finally discuss numerical implementation issues.

Cours slides 

 Cours 4: Nadia Raissi

Titre : Dynamic Optimization Methods Bioeconomic modeling in perspective

Durée : 6h

Nom de l'enseignant : Nadia Raissi

Institution de l'enseignant : Mohammed V University, Rabat 

Pays de l'enseignant : Maroc

Abstract

The expression "sustainable development" has entered popular usage. It refers to a need to organize and control the dynamics and the complex interactions between society and nature, in order to promote their coexistence and their common evolution. Hence the interfaces between economics and ecology merits to be study and this is the purpose of mathematical bioeconomics. Mathematically meaning sustainability can be formulated as the search for a stable ecosystemic balance. The complexity of the different mechanisms involved requires the use of increasingly sophisticated mathematical theories.

The objective of this course is to give the main concepts of dynamic optimization necessary to address the issues of stabilization in the core. Two issues will be addressed through their modeling: sustainable fisheries management and household waste recovery.

Cours 5: ELHAJ EZZAHID

Titre : Introduction to the Ramsey optimal growth model

Durée : 6h

Nom de l'enseignant : ELHAJ

Institution de l'enseignant : Mohammed V University, Rabat 

Pays de l'enseignant : Maroc

Learning objectives

1. Understanding the different flows in a simple economic system ;

2. Mathematical formalization of decisions of agents in an economic system to obtain a general equilibrium;

3. Positing the optimization problem in a dynamic setting and explain the logic of the Ramsey model;

4. Form the Hamiltonian and solve it to have the Euler equation;

5. Interpretation of the results economically;

6. Elaboration of the phase diagram for the optimal control problem when we have one state variable and one control variable;

7. Simulation of the impact of some shocks on the values of c and k at the steady state of an optimal growth model.
   

Cours 6: Alexander Keimer

Titre : Introduction to non local conservation law

Durée : 6h

Nom de l'enseignant : Alexander Keimer

Institution de l'enseignant : Researcher at the Institute of Transportation Studies, UC Berkeley. 

Pays de l'enseignant : USA

Abstract

We will start by illustrating recent challenges regarding routing applications in road networks and the underlying game theoretical components.

With this motivation in mind we discuss linear conservation laws on networks where one can take advantage of explicit solution formulae in terms of characteristics. On each link we define a conservation law. The conservation laws are coupled at the junctions of the network via the boundary conditions. To obtain a suitable and unique network representation we introduce routing functions (satisfying Kirchhoff's law) which are responsible for distributing the flow at the junctions. We generalize to systems of conservation law to integrate ``commodities'' which can model densities with different destinations, or with different driving or routing behavior.

We then discuss some straight forward optimal control problems and game theoretical issues.

Finally, we generalize the dynamics on the links to nonlocal conservation laws. After a short introduction in the well-established theory by means of fixed-point arguments, we then focus on open problem particularly with regard to how to use the nonlocal terms at the junctions to get a reasonable traffic flow models and how to couple multi-commodity models.