43 citations · 73 across the 16 of their papers we have counts for
16 papers
On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces
Benoît Bonnet-Weill, Hélène Frankowska
In this article, we derive conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in…
Carathéodory Theory and A Priori Estimates for Continuity Inclusions in the Space of Probability Measures
Benoît Bonnet-Weill, Hélène Frankowska
In this article, we extend the foundations of the theory of differential inclusions in the space of compactly supported probability measures, introduced recently by the authors, to…
Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces
Benoît Bonnet, Hélène Frankowska
In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable t…
Semiconcavity and Sensitivity Analysis in Mean-Field Optimal Control and Applications
Benoît Bonnet, Hélène Frankowska
In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Buildin…
On the Properties of the Value Function Associated to a Mean-Field Optimal Control Problem of Bolza Type
Benoît Bonnet, Hélène Frankowska
In this paper, we obtain several structural results for the value function associated to a mean-field optimal control problem of Bolza type in the space of measures. After establis…
Necessary Optimality Conditions for Optimal Control Problems in Wasserstein Spaces
Benoît Bonnet, Hélène Frankowska
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To thi…