Section: New Results

Variational problems under divergence constraint - Alg2

• Benamou, Bonne, Carlier - Dynamic problems: we have extended the Augmented Lagrangian method used for the CFD formulation of the Optimal Mass Transportation to Mean Field Games that is for the optimal control of the continuity equation. A freefem Code has been implemented.

• Benamou, Carlier - Static problems with a divergence constraint. We have also extended the Augmented Lagrangian method to static problem where a space divergence constraint appears. This includes the delicate case of the original Monge Optimal Mass Transportation cost (cost=distance) and also Wardrop equilibria in congested transport and related degenerate elliptic equations, like the $p$-Laplacian operator. A freefem Code has been implemented.

  Figure 2. Monge transport flow between sinks and sources.

  Figure 3. Congested transport flows between sink and source.