Necessary optimality conditions for optimal control problems in Wasserstein spaces
B Bonnet, H Frankowska - Applied Mathematics & Optimization, 2021 - Springer
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 this end …
control problem formulated in the Wasserstein space of probability measures. To this end …
Regularized Stein variational gradient flow
The stein variational gradient descent (SVGD) algorithm is a deterministic particle method
for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to …
for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to …
The Pontryagin maximum principle in the Wasserstein space
Abstract We prove a Pontryagin Maximum Principle for optimal control problems in the
space of probability measures, where the dynamics is given by a transport equation with non …
space of probability measures, where the dynamics is given by a transport equation with non …
Ensemble Kalman sampler: Mean-field limit and convergence analysis
The ensemble Kalman sampler (EKS) is a method introduced in Garbuno-Inigo et al., SIAM
J. Appl. Dyn. Syst., 19 (2020), pp. 412--441 to find approximately independent and …
J. Appl. Dyn. Syst., 19 (2020), pp. 412--441 to find approximately independent and …
Consensus formation in first-order graphon models with time-varying topologies
B Bonnet, NP Duteil, M Sigalotti - Mathematical Models and Methods …, 2022 - World Scientific
In this paper, we investigate the asymptotic formation of consensus for several classes of
time-dependent cooperative graphon dynamics. After motivating the use of this type of …
time-dependent cooperative graphon dynamics. After motivating the use of this type of …
Measure-theoretic models for crowd dynamics
B Piccoli, F Rossi - Crowd Dynamics, Volume 1: Theory, Models, and …, 2019 - Springer
This chapter revises some modeling, analysis, and simulation contributions for crowd
dynamics using time-evolving measures. Two key features are strictly related to the use of …
dynamics using time-evolving measures. Two key features are strictly related to the use of …
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast
reactions. It is known that the fast-reaction-rate limit can be described by an ODE with …
reactions. It is known that the fast-reaction-rate limit can be described by an ODE with …
Semiconcavity and sensitivity analysis in mean-field optimal control and applications
B Bonnet, H Frankowska - Journal de Mathématiques Pures et Appliquées, 2022 - Elsevier
In this article, we investigate some of the fine properties of the value function associated with
an optimal control problem in the Wasserstein space of probability measures. Building on …
an optimal control problem in the Wasserstein space of probability measures. Building on …
Intrinsic Lipschitz regularity of mean-field optimal controls
In this article, we provide sufficient conditions under which the controlled vector fields
solution of optimal control problems formulated on continuity equations are Lipschitz regular …
solution of optimal control problems formulated on continuity equations are Lipschitz regular …
Ensemble Kalman inversion for nonlinear problems: weights, consistency, and variance bounds
Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular
sampling methods for obtaining a target posterior distribution. They can be seem as one …
sampling methods for obtaining a target posterior distribution. They can be seem as one …