Y. Achdou, F. J. Buera, J. Lasry, P. Lions, and B. Moll, Partial differential equation models in macroeconomics, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.3, issue.1, p.20130397, 2014.
DOI : 10.2307/2297841

R. Andreev, Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion In preparation, 2016.

L. Ambrosio and A. Figalli, On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations, Calc. Var, PDE, issue.4, pp.31-497, 2008.

L. Ambrosio and A. Figalli, Geodesics in the Space of Measure-Preserving Maps and Plans, Archive for Rational Mechanics and Analysis, vol.5, issue.5, pp.421-462, 2009.
DOI : 10.1007/s00205-008-0189-2

URL : https://hal.archives-ouvertes.fr/hal-00838835

L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics, 2005.

J. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000.
DOI : 10.1007/s002110050002

J. Benamou and G. Carlier, Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations, Journal of Optimization Theory and Applications, vol.111, issue.2, 2015.
DOI : 10.1007/s10957-015-0725-9

G. Bouchitté and G. Buttazzo, New lower semicontinuity results for nonconvex functionals defined on measures, Nonlinear Anal, pp.15-679, 1990.

Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Communications on Pure and Applied Mathematics, vol.111, issue.4, pp.411-452, 1999.
DOI : 10.1002/(SICI)1097-0312(199904)52:4<411::AID-CPA1>3.0.CO;2-3

G. Buttazzo, C. Jimenez, and E. Oudet, An Optimization Problem for Mass Transportation with Congested Dynamics, SIAM Journal on Control and Optimization, vol.48, issue.3, pp.1961-1976, 2010.
DOI : 10.1137/07070543X

URL : https://hal.archives-ouvertes.fr/hal-00385145

P. Cardaliaguet, Weak Solutions for First Order Mean Field Games with Local Coupling, 2013.
DOI : 10.1007/978-3-319-06917-3_5

URL : https://hal.archives-ouvertes.fr/hal-00827957

P. Cardaliaguet, G. Carlier, and B. Nazaret, Geodesics for a class of distances in the space of probability measures, Calc. Var, pp.395-420, 2013.

P. Cardaliaguet and J. Graber, Mean field games systems of first order, ESAIM: Control, Optimisation and Calculus of Variations, vol.21, issue.3, 2015.
DOI : 10.1051/cocv/2014044

URL : https://hal.archives-ouvertes.fr/hal-00925905

P. Cardaliaguet, J. Graber, A. Porretta, and D. Tonon, Second order mean field games with degenerate diffusion and local coupling, Nonlinear Differ, Equ. Appl, vol.22, pp.1287-1317, 2015.

P. Cardaliaguet, A. R. Mészáros, and F. , Santambrogio First order Mean Field Games with density constraints: pressure equals price

G. Carlier, C. Jimenez, and F. Santambrogio, Optimal Transportation with Traffic Congestion and Wardrop Equilibria, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1330-1350, 2008.
DOI : 10.1137/060672832

URL : https://hal.archives-ouvertes.fr/hal-00361010

G. Carlier and F. Santambrogio, A continuous theory of traffic congestion and Wardrop equilibria, Journal of Mathematical Sciences, vol.2, issue.12, pp.792-804, 2010.
DOI : 10.1007/s10958-012-0715-5

I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Classics in Mathematics, Society for Industrial and Applied Mathematics, 1999.
DOI : 10.1137/1.9781611971088

M. Fortin and R. Glowinski, Augmented Lagrangian methods, Applications to the Numerical Solution of Boundary-Value Problems, 1983.

P. J. Graber, Optimal Control of First-Order Hamilton???Jacobi Equations with Linearly Bounded Hamiltonian, Applied Mathematics & Optimization, vol.9, issue.6, pp.185-224, 2014.
DOI : 10.1007/s00245-014-9239-3

URL : https://hal.archives-ouvertes.fr/hal-00871964

J. Lasry and P. Lions, Jeux ?? champ moyen. I ??? Le cas stationnaire, Comptes Rendus Mathematique, vol.343, issue.9, pp.619-625, 2006.
DOI : 10.1016/j.crma.2006.09.019

J. Lasry and P. Lions, JeuxàJeux`Jeuxà champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, issue.10, pp.343-679, 2006.

J. Lasry and P. Lions, Mean field games, Japanese Journal of Mathematics, vol.4, issue.1, pp.229-260, 2007.
DOI : 10.1007/s11537-007-0657-8

URL : https://hal.archives-ouvertes.fr/hal-00667356

B. Maury and A. , A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE, Mathematical Models and Methods in Applied Sciences, vol.20, issue.10, pp.1787-1821, 2010.
DOI : 10.1142/S0218202510004799

URL : https://hal.archives-ouvertes.fr/hal-00418511

A. R. Mészáros and F. J. , Silva A variational approach to second order mean field games with density constraints: the stationary case, J. Math. Pures Appl

A. Prosinski and F. , Santambrogio Global-in-time regularity via duality for congestion-penalized Mean Field Games

F. Santambrogio, A modest proposal for MFG with density constraints, Networks and Heterogeneous Media, vol.7, issue.2, pp.337-347, 2012.
DOI : 10.3934/nhm.2012.7.337

URL : https://hal.archives-ouvertes.fr/hal-00637325

F. Santambrogio, Regularity via duality. Short lecture notes
URL : https://hal.archives-ouvertes.fr/hal-01295289

C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics AMS, vol.58, 2003.
DOI : 10.1090/gsm/058

J. G. Wardrop, CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH., Proceedings of the Institution of Civil Engineers, vol.1, issue.5, pp.325-378, 1952.
DOI : 10.1680/ipeds.1952.11362