Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEsReport as inadecuate




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1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales Inria Paris-Rocquencourt 2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Keywords : Augmented Lagrangian Optimal Transport Monge Problem Mean-Field Games degenerate elliptic PDEs





Author: Jean-David Benamou - Guillaume Carlier -

Source: https://hal.archives-ouvertes.fr/



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