[hal-01073143] Augmented Lagrangian methods for transport optimization Mean-Field Games and degenerate PDEs

Many problems from mass transport can be reformulated as variational problems under a prescribed divergence constraint static problems or subject to a time dependent continuity equation which again can also be formulated as a divergence constraint but in time and space The variational class of Mean-Field Games introduced by Lasry and Lions may also be interpreted as a generalisation of the time-dependent optimal transport problem Following Benamou and Brenier we show that augmented Lagrangian methods are well-suited to treat convex but nonsmooth problems It includes in particular Monge historic optimal transport problem A Finite Element discretization and implementation of the method is used to provide numerical simulations and a convergence study



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