S. Agenent, S. Haker, and A. Tannenbaum, Minimizing Flows for the Monge--Kantorovich Problem, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.61-97, 2003.
DOI : 10.1137/S0036141002410927

J. Benamou, Numerical resolution of an ???unbalanced??? mass transport problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.5, pp.851-868, 2003.
DOI : 10.1051/m2an:2003058

URL : https://hal.archives-ouvertes.fr/inria-00071800

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 Y. Brenier, Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions, Journal of Optimization Theory and Applications, vol.44, issue.2, pp.255-271, 2001.
DOI : 10.1023/A:1011926116573

J. Benamou, Y. Brenier, and K. , The Monge-Kantorovitch mass transfer and its computational fluid mechanics formulation, International Journal for Numerical Methods in Fluids, vol.138, issue.1-2, pp.21-30, 2002.
DOI : 10.1002/fld.264

J. Benamou, . Froese, and . Oberman, Numerical solution of the second boundary value problem for the Elliptic Monge- Ampère equation, 2012.

J. Benamou, B. Froese, and A. Oberman, Numerical Solution of the Optimal Transportation Problem via viscosity solutions for the Monge-Ampère equation, arXiv preprint arXiv, pp.1208-4873, 2012.

E. J. Dean and R. Glowinski, Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type, Computer methods in applied mechanics and engineering, pp.13-161344, 2006.

M. Fortin and R. Glowinski, Augmented Lagrangian Methods: Applications to the Solution of Boundary Value Problems, Studies in Mathematics and its Applications, vol.15, 1983.

G. Loeper and F. Rapetti, Numerical solution of the Monge???Amp??re equation by a Newton's algorithm, Comptes Rendus Mathematique, vol.340, issue.4, pp.319-324, 2005.
DOI : 10.1016/j.crma.2004.12.018

P. Tseng, Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, vol.109, issue.3, pp.475-494, 2001.
DOI : 10.1023/A:1017501703105

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