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Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs

Abstract : 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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https://hal.inria.fr/hal-01073143
Contributor : Jean-David Benamou <>
Submitted on : Friday, October 10, 2014 - 9:42:21 AM
Last modification on : Wednesday, October 14, 2020 - 4:01:14 AM
Long-term archiving on: : Sunday, January 11, 2015 - 10:11:07 AM

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Jean-David Benamou, Guillaume Carlier. Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs. 2014. ⟨hal-01073143⟩

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