Bibliography

Major publications by the team in recent years

1J.-D. Benamou.

Numerical resolution of an “unbalanced” mass transport problem, in: M2AN Math. Model. Numer. Anal., 2003, vol. 37, n^o 5, pp. 851–868.

http://dx.doi.org/10.1051/m2an:2003058
2J.-D. Benamou, Y. Brenier.

A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, in: Numer. Math., 2000, vol. 84, n^o 3, pp. 375–393.

http://dx.doi.org/10.1007/s002110050002
3J.-D. Benamou, Y. Brenier.

Mixed $L^{2}$ -Wasserstein optimal mapping between prescribed density functions, in: J. Optim. Theory Appl., 2001, vol. 111, n^o 2, pp. 255–271.

http://dx.doi.org/10.1023/A:1011926116573
4J.-D. Benamou, Y. Brenier.

Weak existence for the semigeostrophic equations formulated as a coupled Monge-Ampère/transport problem, in: SIAM J. Appl. Math., 1998, vol. 58, n^o 5, pp. 1450–1461.

http://dx.doi.org/10.1137/S0036139995294111
5J.-D. Benamou, Y. Brenier, K. Guittet.

Numerical analysis of a multi-phasic mass transport problem, in: Recent advances in the theory and applications of mass transport, Providence, RI, Contemp. Math., Amer. Math. Soc., 2004, vol. 353, pp. 1–17.
6J.-D. Benamou, B. D. Froese, A. M. Oberman.

Numerical solution of the Optimal Transportation problem using the Monge-Ampère equation, in: J. Comput. Physics, 2014, to appear.
7F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio.

Numerical approximation of continuous traffic congestion equilibria, in: Netw. Heterog. Media, 2009, vol. 4, n^o 3, pp. 605–623.

http://dx.doi.org/10.3934/nhm.2009.4.605
8A. Blanchet, G. Carlier.

Optimal Transport and Cournot-Nash Equilibria, 2012.
9L. Brasco, G. Carlier, F. Santambrogio.

Congested traffic dynamics, weak flows and very degenerate elliptic equations [corrected version of MR2584740], in: J. Math. Pures Appl. (9), 2010, vol. 93, n^o 6, pp. 652–671.

http://dx.doi.org/10.1016/j.matpur.2010.03.010
10G. Buttazzo, G. Carlier.

Optimal spatial pricing strategies with transportation costs, in: Nonlinear analysis and optimization II. Optimization, Providence, RI, Contemp. Math., Amer. Math. Soc., 2010, vol. 514, pp. 105–121.
11G. Carlier.

A general existence result for the principal-agent problem with adverse selection, in: J. Math. Econom., 2001, vol. 35, n^o 1, pp. 129–150.

http://dx.doi.org/10.1016/S0304-4068(00)00057-4
12G. Carlier, I. Ekeland.

Matching for teams, in: Econom. Theory, 2010, vol. 42, n^o 2, pp. 397–418.

http://dx.doi.org/10.1007/s00199-008-0415-z
13G. Carlier, A. Galichon, F. Santambrogio.

From Knothe's transport to Brenier's map and a continuation method for optimal transport, in: SIAM J. Math. Anal., 2009/10, vol. 41, n^o 6, pp. 2554–2576.

http://dx.doi.org/10.1137/080740647

Publications of the year

Articles in International Peer-Reviewed Journals

14J.-D. Benamou, F. Collino, S. Marmorat.

Numerical Microlocal analysis of 2-D noisy harmonic plane and circular waves, in: Asymptotic Analysis, 2013, vol. 83, n^o 1-2, pp. 157–187. [ DOI : 10.3233/ASY-121157 ]

http://hal.inria.fr/hal-00937691

Internal Reports

15J.-D. Benamou, G. Carlier, N. Bonne.

An Augmented Lagrangian Numerical approach to solving Mean-Fields Games, December 2013, 30 p.

http://hal.inria.fr/hal-00922349

References in notes

16M. Agueh.

Global weak solutions to kinetic models of granular media, 2013.
17S. Angenent, S. Haker, A. Tannenbaum.

Minimizing flows for the Monge-Kantorovich problem, in: SIAM J. Math. Anal., 2003, vol. 35, n^o 1, pp. 61–97.

http://dx.doi.org/10.1137/S0036141002410927
18F. Aurenhammer.

Power diagrams: properties, algorithms and applications, in: SIAM J. Comput., 1987, vol. 16, n^o 1, pp. 78–96.

http://dx.doi.org/10.1137/0216006
19J.-D. Benamou, F. Castella, T. Katsaounis, B. Perthame.

High frequency limit of the Helmholtz equations, in: Rev. Mat. Iberoamericana, 2002, vol. 18, n^o 1, pp. 187–209.

http://dx.doi.org/10.4171/RMI/315
20F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio.

Numerical approximation of continuous traffic congestion equilibria, in: Netw. Heterog. Media, 2009, vol. 4, n^o 3, pp. 605–623.

http://dx.doi.org/10.3934/nhm.2009.4.605
21D. P. Bertsekas.

Auction algorithms for network flow problems: a tutorial introduction, in: Comput. Optim. Appl., 1992, vol. 1, n^o 1, pp. 7–66.

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22Y. Brenier.

Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations, in: J. Nonlinear Sci., 2009, vol. 19, n^o 5, pp. 547–570.

http://dx.doi.org/10.1007/s00332-009-9044-3
23Y. Brenier.

Décomposition polaire et réarrangement monotone des champs de vecteurs, in: C. R. Acad. Sci. Paris Sér. I Math., 1987, vol. 305, n^o 19, pp. 805–808.
24Y. Brenier.

Polar factorization and monotone rearrangement of vector-valued functions, in: Comm. Pure Appl. Math., 1991, vol. 44, n^o 4, pp. 375–417.

http://dx.doi.org/10.1002/cpa.3160440402
25Y. Brenier, U. Frisch, M. Henon, G. Loeper, S. Matarrese, R. Mohayaee, A. Sobolevskii.

Reconstruction of the early universe as a convex optimization problem, in: Mon.Not.Roy.Astron.Soc., 2003, vol. 346, pp. 501–524.

http://arxiv.org/pdf/astro-ph/0304214.pdf
26G. Buttazzo, L. De Pascale, P. Gori-Giorgi.

Optimal-transport formulation of electronic density-functional theory, in: Phys. Rev. A, Jun 2012, vol. 85, 062502 p.

http://link.aps.org/doi/10.1103/PhysRevA.85.062502
27G. Buttazzo, C. Jimenez, É. Oudet.

An optimization problem for mass transportation with congested dynamics, in: SIAM J. Control Optim., 2009, vol. 48, n^o 3, pp. 1961–1976.

http://dx.doi.org/10.1137/07070543X
28G. Buttazzo, F. Santambrogio.

A mass transportation model for the optimal planning of an urban region, in: SIAM Rev., 2009, vol. 51, n^o 3, pp. 593–610.

http://dx.doi.org/10.1137/090759197
29L. A. Caffarelli.

The regularity of mappings with a convex potential, in: J. Amer. Math. Soc., 1992, vol. 5, n^o 1, pp. 99–104.

http://dx.doi.org/10.2307/2152752
30L. A. Caffarelli, R. J. McCann.

Free boundaries in optimal transport and Monge-Ampère obstacle problems, in: Ann. of Math. (2), 2010, vol. 171, n^o 2, pp. 673–730.

http://dx.doi.org/10.4007/annals.2010.171.673
31E. A. Carlen, W. Gangbo.

Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric, in: Arch. Ration. Mech. Anal., 2004, vol. 172, n^o 1, pp. 21–64.

http://dx.doi.org/10.1007/s00205-003-0296-z
32L. Chacón, G. L. Delzanno, J. M. Finn.

Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution, in: J. Comput. Phys., 2011, vol. 230, n^o 1, pp. 87–103.

http://dx.doi.org/10.1016/j.jcp.2010.09.013
33F. A. C. C. Chalub, P. A. Markowich, B. Perthame, C. Schmeiser.

Kinetic models for chemotaxis and their drift-diffusion limits, in: Monatsh. Math., 2004, vol. 142, n^o 1-2, pp. 123–141.

http://dx.doi.org/10.1007/s00605-004-0234-7
34P.-A. Chiappori, R. J. McCann, L. P. Nesheim.

Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness, in: Econom. Theory, 2010, vol. 42, n^o 2, pp. 317–354.

http://dx.doi.org/10.1007/s00199-009-0455-z
35J.-F. Cossette, P. K. Smolarkiewicz.

A Monge-Ampère enhancement for semi-Lagrangian methods, in: Comput. & Fluids, 2011, vol. 46, pp. 180–185.

http://dx.doi.org/10.1016/j.compfluid.2011.01.029
36C. Cotar, G. Friesecke, C. Kl¸ppelberg.

Density Functional Theory and Optimal Transportation with Coulomb Cost, in: Communications on Pure and Applied Mathematics, 2013, vol. 66, n^o 4, pp. 548–599.

http://dx.doi.org/10.1002/cpa.21437
37M. J. P. Cullen, W. Gangbo, G. Pisante.

The semigeostrophic equations discretized in reference and dual variables, in: Arch. Ration. Mech. Anal., 2007, vol. 185, n^o 2, pp. 341–363.

http://dx.doi.org/10.1007/s00205-006-0040-6
38M. J. P. Cullen, J. Norbury, R. J. Purser.

Generalised Lagrangian solutions for atmospheric and oceanic flows, in: SIAM J. Appl. Math., 1991, vol. 51, n^o 1, pp. 20–31.

http://dx.doi.org/10.1137/0151002
39M. J. P. Cullen, R. J. Purser.

An extended Lagrangian theory of semigeostrophic frontogenesis, in: J. Atmospheric Sci., 1984, vol. 41, n^o 9, pp. 1477–1497.

http://dx.doi.org/10.1175/1520-0469(1984)041<1477:AELTOS>2.0.CO;2
40B. Engquist, B. D. Froese.

Application of the Wasserstein metric to seismic signals, 2013, Preprint.
41A. Figalli.

The optimal partial transport problem, in: Arch. Ration. Mech. Anal., 2010, vol. 195, n^o 2, pp. 533–560.

http://dx.doi.org/10.1007/s00205-008-0212-7
42A. Figalli, R. Mc Cann, Y. Kim.

When is multi-dimensional screening a convex program?, in: Journal of Economic Theory, 2011.
43M. Fortin, R. Glowinski.

Augmented Lagrangian methods, Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam, 1983, vol. 15, xix+340 p, Applications to the numerical solution of boundary value problems, Translated from the French by B. Hunt and D. C. Spicer.
44U. Frisch, S. Matarrese, R. Mohayaee, 2. Sobolevski.

Monge-Ampère-Kantorovitch (MAK) reconstruction of the eary universe, in: Nature, 2002, vol. 417, n^o 260.
45B. D. Froese, A. M. Oberman.

Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher, in: SIAM J. Numer. Anal., 2011, vol. 49, n^o 4, pp. 1692–1714.

http://dx.doi.org/10.1137/100803092
46A. Galichon, P. Henry-Labordère, N. Touzi.

A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Loopback options, 2011, submitted to Annals of Applied Probability.
47A. Galichon, B. Salanié.

Matchings with Trade-Offs: Revealed preferences over Competing Characteristics, 2010, preprint.
48A. Galichon, B. Salanié.

Cupid's invisible hand: Social Surplus and Identification in Matching Models, 2011, preprint.
49W. Gangbo, A. Świȩch.

Optimal maps for the multidimensional Monge-Kantorovich problem, in: Comm. Pure Appl. Math., 1998, vol. 51, n^o 1, pp. 23–45.

http://dx.doi.org/10.1002/(SICI)1097-0312(199801)51:1<23::AID-CPA2>3.0.CO;2-H
50C. E. Gutiérrez.

The Monge-Ampère equation, Progress in Nonlinear Differential Equations and their Applications, 44, Birkhäuser Boston Inc., Boston, MA, 2001, xii+127 p.

http://dx.doi.org/10.1007/978-1-4612-0195-3
51B. J. Hoskins.

The mathematical theory of frontogenesis, in: Annual review of fluid mechanics, Vol. 14, Palo Alto, CA, Annual Reviews, 1982, pp. 131–151.
52R. Jordan, D. Kinderlehrer, F. Otto.

The variational formulation of the Fokker-Planck equation, in: SIAM J. Math. Anal., 1998, vol. 29, n^o 1, pp. 1–17.

http://dx.doi.org/10.1137/S0036141096303359
53W. Jäger, S. Luckhaus.

On explosions of solutions to a system of partial differential equations modelling chemotaxis, in: Trans. Amer. Math. Soc., 1992, vol. 329, n^o 2, pp. 819–824.

http://dx.doi.org/10.2307/2153966
54L. Kantorovitch.

On the translocation of masses, in: C. R. (Doklady) Acad. Sci. URSS (N.S.), 1942, vol. 37, pp. 199–201.
55J.-M. Lasry, P.-L. Lions.

Mean field games, in: Jpn. J. Math., 2007, vol. 2, n^o 1, pp. 229–260.

http://dx.doi.org/10.1007/s11537-007-0657-8
56B. Li, F. Habbal, M. Ortiz.

Optimal transportation meshfree approximation schemes for ﬂuid and plastic ﬂows, in: Int. J. Numer. Meth. Engng 83:1541–1579, 2010, vol. 83, pp. 1541–1579.
57G. Loeper.

A fully nonlinear version of the incompressible Euler equations: the semigeostrophic system, in: SIAM J. Math. Anal., 2006, vol. 38, n^o 3, pp. 795–823.

http://dx.doi.org/10.1137/050629070
58X.-N. Ma, N. S. Trudinger, X.-J. Wang.

Regularity of potential functions of the optimal transportation problem, in: Arch. Ration. Mech. Anal., 2005, vol. 177, n^o 2, pp. 151–183.

http://dx.doi.org/10.1007/s00205-005-0362-9
59B. Maury, A. Roudneff-Chupin, F. Santambrogio.

A macroscopic crowd motion model of gradient flow type, in: Math. Models Methods Appl. Sci., 2010, vol. 20, n^o 10, pp. 1787–1821.

http://dx.doi.org/10.1142/S0218202510004799
60J.-M. Mirebeau, J. Fehrenbach.

Sparse Non-Negative Stencils for Anisotropic Diffusion, 2013, Preprint.
61Q. Mérigot.

A comparison of two dual methods for discrete optimal transport, in: Geometric Science of Information, LNCS 8085, 389-396, 2013.
62Q. Mérigot.

A multiscale approach to optimal transport, in: Computer Graphics Forum, 2011, vol. 30, n^o 5, pp. 1583–1592.
63Q. Mérigot.

A Comparison of Two Dual Methods for Discrete Optimal Transport, in: Geometric Science of Information, Springer Berlin Heidelberg, 2013, pp. 389–396.
64G. P. Nicolas Papadakis, É. Oudet.

Optimal Transport with Proximal Splitting, 2013, Preprint.
65J. Nieto, F. Poupaud, J. Soler.

High-field limit for the Vlasov-Poisson-Fokker-Planck system, in: Arch. Ration. Mech. Anal., 2001, vol. 158, n^o 1, pp. 29–59.

http://dx.doi.org/10.1007/s002050100139
66V. I. Oliker, L. D. Prussner.

On the numerical solution of the equation $(\partial^{2} z / \partial x^{2}) (\partial^{2} z / \partial y^{2}) - {((\partial^{2} z / \partial x \partial y))}^{2} = f$ and its discretizations. I, in: Numer. Math., 1988, vol. 54, n^o 3, pp. 271–293.

http://dx.doi.org/10.1007/BF01396762
67B. Pass.

Convexity and multi-dimensional screening for spaces with different dimensions, in: J. Econom. Theory, 2012, vol. 147, n^o 6, pp. 2399–2418.

http://dx.doi.org/10.1016/j.jet.2012.05.004
68B. Pass.

On the local structure of optimal measures in the multi-marginal optimal transportation problem, in: Calc. Var. Partial Differential Equations, 2012, vol. 43, n^o 3-4, pp. 529–536.

http://dx.doi.org/10.1007/s00526-011-0421-z
69B. Pass.

On a Class of Optimal Transportation Problems with Infinitely Many Marginals, in: SIAM J. Math. Anal., 2013, vol. 45, n^o 4, pp. 2557–2575.

http://dx.doi.org/10.1137/120881427
70B. Pass.

Optimal transportation with infinitely many marginals, in: J. Funct. Anal., 2013, vol. 264, n^o 4, pp. 947–963.

http://dx.doi.org/10.1016/j.jfa.2012.12.002
71A. V. Pogorelov.

Generalized solutions of Monge-Ampère equations of elliptic type, in: A tribute to IlyA Bakelman (College Station, TX, 1993), College Station, TX, Discourses Math. Appl., Texas A & M Univ., 1994, vol. 3, pp. 47–50.
72C. Prins, J.H.M. Thije Boonkkamp, J. van. Roosmalen, W. IJzerman, T. Tukker.

A numerical method for the design of free-form reflectors for lighting applications, in: External Report, CASA Report, No. 13-22, 2013.

http://www.win.tue.nl/analysis/reports/rana13-22.pdf
73J. Rabin, G. Peyré, J. Delon, M. Bernot.

Wassertein Barycenter and its Applications to Texture Mixing, in: LNCS, Proc. SSVM'11, Springer, 2011, vol. 6667, pp. 435–446. [ DOI : 10.1007/978-3-642-24785-9 ]

http://hal.archives-ouvertes.fr/hal-00476064/
74B. Salanié.

The Economics of Contracts: a Primer, MIT Press, 1997.
75C. Villani.

Optimal transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2009, vol. 338, xxii+973 p, Old and new.

http://dx.doi.org/10.1007/978-3-540-71050-9
76L. Zhu, Y. Yang, S. Haker, A. Tannenbaum.

An image morphing technique based on optimal mass preserving mapping, in: IEEE Trans. Image Process., 2007, vol. 16, n^o 6, pp. 1481–1495.

http://dx.doi.org/10.1109/TIP.2007.896637

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