Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2014

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.
Fichier principal
Vignette du fichier
ALG2_Draft.pdf (3.29 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01073143 , version 1 (10-10-2014)

Identifiers

  • HAL Id : hal-01073143 , version 1

Cite

Jean-David Benamou, Guillaume Carlier. Augmented Lagrangian methods for transport optimization, Mean-Field Games and degenerate PDEs. 2014. ⟨hal-01073143⟩
714 View
1590 Download

Share

Gmail Facebook X LinkedIn More