Applied Mathematics & Optimization

, Volume 74, Issue 3, pp 535–578 | Cite as

Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method

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Abstract

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditions are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.

Keywords

Mean Field Type Control Congestion Augmented Lagrangian Finite Difference Schemes 

Mathematics Subject Classification

49K20 49M20 65K10 65M06 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRSUniv. Paris Diderot, Sorbonne Paris CitéParisFrance

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