Reminder: Mattia Bongini's seminar at SISSA

[Emanuele Tuillier Illingworth]

> SEMINAR ANNOUNCEMENT
>
> Mattia Bongini (TU München)
>
> TITLE
> Mean-field Pontryagin maximum principle
>
> ABSTRACT
> The mean-field approach is a powerful tool for giving sense to the 
> notion that a discrete dynamical system converges to a continuous one 
> as the number of agents increases. This technique has been recently 
> used in connection with $\Gamma$-convergence to show that a 
> two-populations discrete optimal control problem converges to an 
> ODE-PDE constrainted optimal control problem: in this model, a 
> discrete population of agents (called "leaders") interacts with a 
> continuous one (the mass of "followers"), and its target is to steer 
> the entire population towards configurations minimizing a given cost. 
> In this paper we address the problem of deriving optimality conditions 
> for this optimal control problem. We show that these optimality 
> conditions can be seen as the mean-field limit $N\to\infty$ of the 
> Pontryagin Maximum Principle applied to the two-population discrete 
> system with $N$ followers. This, in turn, enables us a constructive 
> method to derive solutions as limits of solutions of the discrete 
> optimality conditions, which in the end let us establish existence 
> results for these kinds of Hamiltonian systems. Finally, we prove that 
> the resulting optimality conditions are indeed Hamiltonian flows in 
> the Wasserstein space of probability measures.
>
> Venue: SISSA, room 005 (ground floor), Thursday 19 March at 11:00
>