Patrimony

The Louis Bachelier Group's patrimony has been defined as all the publications produced by academic researchers thanks to Group funding (ILB, FdR, IEF, Labex) or via the use of EquipEx data (BEDOFIH, EUROFIDAI).


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On the long time behavior of potential MFG.

Contrôl optimal, Jeux à champ moyen, Mean Field Games, Optimal Control, Théorie KAM faible, Weak KAM theory

Hamilton–Jacobi equations for optimal control on junctions and networks.

Hamilton-Jacobi equations, Networks, Optimal control, Viscosity solutions

Hamilton-Jacobi Equations on Networks as Limits of Singularly Perturbed Problems in Optimal Control: Dimension Reduction.

Dimension reduction, Graphs, Hamilton-Jacobi equations, Networks, Optimal control, Singular perturbation, Viscosity solutions

Stochastic homogenization of some interface propagation problems.

Approximation numérique, Contrôle optimal, Equations de Hamilton-Jacobi, Front propagation, Hamilton-Jacobi equations, Homogénéisation stochastique, Metric problem, Numerical approximation, Optimal control, Problème métrique, Propagations de fronts, Stochastic homogenization, Viscosity solutions

Learning in medium field games.

Algorithme de descente miroir, Contrôle optimal, Fictitious play, Jeux à champ moyen, Mean field games, Online mirror descent algorithm, Optimal control

Hamilton-Jacobi equations constrained on networks.

Graphs, Hamilton-Jacobi equations, Networks, Optimal control, Viscosity solutions

Hamilton-Jacobi equations on heterogeneous networks or structures.

Contrôle optimal, Hamilton-Jacobi equation, Jonction, Junction, Network, Optimal control, Perturbation singulière, Réseau, Singular perturbation, Solution de viscosité, Viscosity solution, Équation de Hamilton-Jacobi

Computation and implementation of an optimal mean field control for smart charging.

Optimal control, Smart charging

Mean field games systems of first order.

Hamilton-Jacobi equations, Long time average, Mean field games, Nonlinear PDE, Optimal control, Transport theory

Mean field games systems of first order.

Hamilton-Jacobi equations, Long time average, Mean field games, Nonlinear PDE, Optimal control, Transport theory

Optimal control in Wasserstein spaces.

Alignment problems, Analyse non-Lisse, Calcul sous-Différentiel métrique, Contrôle optimal, Espaces de Wasserstein, Géométrie sous-Riemannienne, Limite de champs moyen, Lipschitz regularity, Mean-Field limit, Multi-Agent systems, Non-Smooth analysis, Optimal control, Optimal transport, Persistance d'excitations, Persistency of excitation, Problèmes d'alignement, Régularité Lipschitz, Singularity theory, Sub-Riemannian geometry, Subdifferential calculus in metric spaces, Systèmes multi-Agents, Théorie des singularités, Transport optimal, Wasserstein spaces

Dynamic optimal control for distress large financial networks and Mean field systems with jumps.

BSDEs with jumps, Contagion de défauts, Contrôle optimal, Default contagion, EDSRs à champs moyen avec sauts, Financial networks, Graphes aléatoires, Mean field BSDEs, Optimal control, Random graphs, Risque systémique, Réseaux financiers, Systemic risk