Francisco Silva

Francisco Silva

• Main host organisation: Università Degli Studi di Roma - La Sapienza, Italy
• Supervisor: Italo Capuzzo Dolcetta
• Secondment organisation: Inria Saclay Ile de France, France
• Nationality: Chilean
• Fellowship duration: April 2011 - August 2012
• Email address

• Background: Francisco holds a master's degree in mathematical engineering from the University of Chile and a PhD from Ecole Polytechnique. His PhD thesis subject was: "Interior penalty approximation for optimal control problems. Optimality conditions in stochastic optimal control theory."

SADCO Project title: Mean field games

Mathematical models in the framework of control and differential games theory provide fundamental qualitative, computational and simulations tools in different branches of engineering, economy and, more recently, social sciences. When these models incorporate decision features (optimization of some performance index, Nash or Pareto equilibria, ...) one has to face problems concerning the qualitative and numerical analysis of nonlinear elliptic and/or parabolic partial differential equations (or systems of) of Hamilton-Jacobi-Isaacs type. This is a very recent research topic where few results have been obtained. The methodology of viscosity solutions has proved to be an effective tool in this respect. Extremely interesting advances, both from the modelling and theoretical point of view, in this active research field are provided by the theory of Mean Field Games recently developed by J.-M Lasry and P.-L. Lions. We plan to develop methods for the approximation and the computation of the solutions of the system of Hamilton-Jacobi-Isaacs partial differential equations arising in the context of Mean Field Games theory. The first results of research in this very promising direction have been recently obtained by Achdou-Capuzzo Dolcetta.

SADCO related publications