L. Ambrosio, Lecture Notes on Optimal Transport Problems, Mathematical Aspects of Evolving Interfaces, pp.1-52, 2003.
DOI : 10.1007/978-3-540-39189-0_1

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

L. Ambrosio, N. Gigli, and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in Math. Birkhäuser, 2008.

S. Angenent, 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

URL : http://iie.fing.edu.uy/investigacion/grupos/gti/seminario/simposio/tannembaum/mk_final.pdf

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, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré, Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.1111-1138, 2015.
DOI : 10.1137/141000439

URL : https://hal.archives-ouvertes.fr/hal-01096124

J. Benamou, G. Carlier, Q. Mérigot, and E. Oudet, Discretization of functionals involving the Monge???Amp??re operator, Numerische Mathematik, vol.7, issue.5, pp.3-611, 2016.
DOI : 10.1093/imrn/rnr076

URL : http://arxiv.org/pdf/1408.4536.pdf

J. Benamou, F. Collino, and J. Mirebeau, Monotone and consistent discretization of the Monge-Amp??re operator, Mathematics of Computation, vol.85, issue.302, pp.302-2743, 2016.
DOI : 10.1090/mcom/3080

URL : http://arxiv.org/pdf/1409.6694

J. M. Borwein and A. S. Lewis, Decomposition of multivariate functions. Canad, J. Math, vol.44, issue.3, pp.463-482, 1992.
DOI : 10.4153/cjm-1992-030-9

J. M. Borwein, A. S. Lewis, and R. D. Nussbaum, Entropy Minimization, DAD Problems, and Doubly Stochastic Kernels, Journal of Functional Analysis, vol.123, issue.2, pp.264-307, 1994.
DOI : 10.1006/jfan.1994.1089

URL : https://doi.org/10.1006/jfan.1994.1089

Y. Brenier, Décomposition polaire et réarrangement monotone de champs de vecteurs, C. R. Acad. Sci. Paris, vol.305, issue.19, pp.805-808, 1987.

Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, vol.117, issue.4, pp.375-417, 1991.
DOI : 10.1002/cpa.3160440402

L. A. Caffarelli, M. Feldman, and R. J. Mccann, Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs, Journal of the American Mathematical Society, vol.15, issue.01, pp.1-1, 2002.
DOI : 10.1090/S0894-0347-01-00376-9

G. Carlier, V. Duval, G. Peyré, and B. Schmitzer, Convergence of Entropic Schemes for Optimal Transport and Gradient Flows, SIAM Journal on Mathematical Analysis, vol.49, issue.2, pp.1385-1418, 2017.
DOI : 10.1137/15M1050264

URL : https://hal.archives-ouvertes.fr/hal-01246086

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in Neural Information Processing Systems (2013), pp.2292-2300

D. Pascale, L. Louet, J. Santambrogio, and F. , The Monge problem with vanishing gradient penalization: Vortices and asymptotic profile, Journal de Math??matiques Pures et Appliqu??es, vol.106, issue.2, pp.237-279, 2016.
DOI : 10.1016/j.matpur.2016.02.009

URL : https://hal.archives-ouvertes.fr/hal-01052294

M. Feldman and R. J. Mccann, Uniqueness and transport density in Monge's mass transportation problem, Calculus of Variations and Partial Differential Equations, vol.15, issue.1, pp.81-113, 2002.
DOI : 10.1007/s005260100119

W. Gangbo and R. J. Mccann, The geometry of optimal transportation, Acta Mathematica, vol.177, issue.2, pp.113-161, 1996.
DOI : 10.1007/BF02392620

URL : http://doi.org/10.1007/bf02392620

L. V. Kantorovich, On the Translocation of Masses, Journal of Mathematical Sciences, vol.133, issue.4, pp.199-201, 1942.
DOI : 10.1007/s10958-006-0049-2

L. Kantorovich, On a problem of Monge. Uspekhi Math, Nauk, vol.3, pp.225-226, 1948.
DOI : 10.1007/s10958-006-0050-9

C. Léonard, From the Schr??dinger problem to the Monge???Kantorovich problem, Journal of Functional Analysis, vol.262, issue.4, pp.1879-1920, 2012.
DOI : 10.1016/j.jfa.2011.11.026

C. Léonard, A survey of the Schr??dinger problem and some of its connections with optimal transport, Discrete and Continuous Dynamical Systems, vol.34, issue.4, pp.1533-1574, 2014.
DOI : 10.3934/dcds.2014.34.1533

B. Lévy, Semi-Discrete Optimal Transport in 3D, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, pp.1693-1715, 2015.
DOI : 10.1007/978-3-540-71050-9

Q. Li, F. Santambrogio, W. , and X. , Regularity in Monge's mass transfer problem, Journal de Math??matiques Pures et Appliqu??es, vol.102, issue.6, pp.1015-1040, 2014.
DOI : 10.1016/j.matpur.2014.03.001

, A multiscale approach to optimal transport, Computer Graphics Forum, vol.30, issue.5, pp.1583-1592, 2011.

G. Monge, Mémoire sur la théorie des déblais et des remblais, Histoire de l'Académie Royale des Sciences de Paris. 1781, pp.666-704

L. Nenna, Numerical Methods for Multi-Marginal Optimal Transportation, 2016.
URL : https://hal.archives-ouvertes.fr/tel-01471589

F. Santambrogio, Optimal Transport for Applied Mathematicians. Birkhäuser

E. Schrödinger, Über die Umkehrung der Naturgesetze (in German), Preuss. Akad. Wiss. Berlin. Phys. Math, vol.144, pp.144-153, 1931.

N. S. Trudinger, W. , and X. , On the Monge mass transfer problem, Calculus of Variations and Partial Differential Equations, vol.13, issue.1, pp.19-31, 2001.
DOI : 10.1007/PL00009922

C. Villani, Topics in Optimal Transportation Graduate Studies in Mathematics. AMS, vol.58, 2003.

C. Villani, of Grund. Math. Wiess

C. Ceremade,