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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, no 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, no 3, pp. 375–393.

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

    Mixed L2-Wasserstein optimal mapping between prescribed density functions, in: J. Optim. Theory Appl., 2001, vol. 111, no 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, no 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, G. Carlier, M. Cuturi, L. Nenna, G. Peyré.

    Iterative Bregman Projections for Regularized Transportation Problems, in: SIAM J. Sci. Comp., 2015, forthcoming.
  • 7J.-D. Benamou, B. D. Froese, A. M. Oberman.

    Numerical solution of the Optimal Transportation problem using the Monge–Ampère equation, in: Journal of Computational Physics, March 2014, vol. 260, no 1, pp. 107–126. [ DOI : 10.1016/j.jcp.2013.12.015 ]

    https://hal.inria.fr/hal-01115626
  • 8F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio.

    Numerical approximation of continuous traffic congestion equilibria, in: Netw. Heterog. Media, 2009, vol. 4, no 3, pp. 605–623.

    http://dx.doi.org/10.3934/nhm.2009.4.605
  • 9A. Blanchet, G. Carlier.

    Optimal Transport and Cournot-Nash Equilibria, 2012, forthcoming.
  • 10L. 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, no 6, pp. 652–671.

    http://dx.doi.org/10.1016/j.matpur.2010.03.010
  • 11G. 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.
  • 12G. Carlier.

    A general existence result for the principal-agent problem with adverse selection, in: J. Math. Econom., 2001, vol. 35, no 1, pp. 129–150.

    http://dx.doi.org/10.1016/S0304-4068(00)00057-4
  • 13G. Carlier, I. Ekeland.

    Matching for teams, in: Econom. Theory, 2010, vol. 42, no 2, pp. 397–418.

    http://dx.doi.org/10.1007/s00199-008-0415-z
  • 14G. 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, no 6, pp. 2554–2576.

    http://dx.doi.org/10.1137/080740647
  • 15C. Prins, J.H.M. Thije Boonkkamp, J. van. Roosmalen, W.L. IJzerman, T.W. 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
Publications of the year

Articles in International Peer-Reviewed Journals

  • 16J.-D. Benamou, B. D. Froese, A. M. Oberman.

    Numerical solution of the Optimal Transportation problem using the Monge–Ampère equation, in: Journal of Computational Physics, March 2014, vol. 260, no 1, pp. 107–126. [ DOI : 10.1016/j.jcp.2013.12.015 ]

    https://hal.inria.fr/hal-01115626
  • 17V. Duval, G. Peyré.

    Exact Support Recovery for Sparse Spikes Deconvolution, in: Foundations of Computational Mathematics, 2014, 43 p.

    https://hal.archives-ouvertes.fr/hal-00839635

Other Publications

References in notes
  • 30S. Angenent, S. Haker, A. Tannenbaum.

    Minimizing flows for the Monge-Kantorovich problem, in: SIAM J. Math. Anal., 2003, vol. 35, no 1, pp. 61–97.

    http://dx.doi.org/10.1137/S0036141002410927
  • 31F. Aurenhammer.

    Power diagrams: properties, algorithms and applications, in: SIAM J. Comput., 1987, vol. 16, no 1, pp. 78–96.

    http://dx.doi.org/10.1137/0216006
  • 32F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio.

    Numerical approximation of continuous traffic congestion equilibria, in: Netw. Heterog. Media, 2009, vol. 4, no 3, pp. 605–623.

    http://dx.doi.org/10.3934/nhm.2009.4.605
  • 33D. P. Bertsekas.

    Auction algorithms for network flow problems: a tutorial introduction, in: Comput. Optim. Appl., 1992, vol. 1, no 1, pp. 7–66.

    http://dx.doi.org/10.1007/BF00247653
  • 34Y. Brenier.

    Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations, in: J. Nonlinear Sci., 2009, vol. 19, no 5, pp. 547–570.

    http://dx.doi.org/10.1007/s00332-009-9044-3
  • 35Y. Brenier.

    Décomposition polaire et réarrangement monotone des champs de vecteurs, in: C. R. Acad. Sci. Paris Sér. I Math., 1987, vol. 305, no 19, pp. 805–808.
  • 36Y. Brenier.

    Polar factorization and monotone rearrangement of vector-valued functions, in: Comm. Pure Appl. Math., 1991, vol. 44, no 4, pp. 375–417.

    http://dx.doi.org/10.1002/cpa.3160440402
  • 37Y. 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
  • 38G. Buttazzo, L. De Pascale, P. Gori-Giorgi.

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

    http://link.aps.org/doi/10.1103/PhysRevA.85.062502
  • 39G. Buttazzo, C. Jimenez, E. Oudet.

    An optimization problem for mass transportation with congested dynamics, in: SIAM J. Control Optim., 2009, vol. 48, no 3, pp. 1961–1976.

    http://dx.doi.org/10.1137/07070543X
  • 40G. Buttazzo, F. Santambrogio.

    A mass transportation model for the optimal planning of an urban region, in: SIAM Rev., 2009, vol. 51, no 3, pp. 593–610.

    http://dx.doi.org/10.1137/090759197
  • 41L. A. Caffarelli.

    The regularity of mappings with a convex potential, in: J. Amer. Math. Soc., 1992, vol. 5, no 1, pp. 99–104.

    http://dx.doi.org/10.2307/2152752
  • 42L. A. Caffarelli, S. Kochengin, V. I. Oliker.

    On the numerical solution of the problem of reflector design with given far-field scattering data, in: Monge Ampère equation: applications to geometry and optimization (Deerfield Beach, FL, 1997), Providence, RI, Contemp. Math., Amer. Math. Soc., 1999, vol. 226, pp. 13–32.

    http://dx.doi.org/10.1090/conm/226/03233
  • 43L. Chacón, G. L. Delzanno, J. M. Finn.

    Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution, in: J. Comput. Phys., 2011, vol. 230, no 1, pp. 87–103.

    http://dx.doi.org/10.1016/j.jcp.2010.09.013
  • 44F. 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, no 1-2, pp. 123–141.

    http://dx.doi.org/10.1007/s00605-004-0234-7
  • 45P.-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, no 2, pp. 317–354.

    http://dx.doi.org/10.1007/s00199-009-0455-z
  • 46J.-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
  • 47C. Cotar, G. Friesecke, C. Kluppelberg.

    Density Functional Theory and Optimal Transportation with Coulomb Cost, in: Communications on Pure and Applied Mathematics, 2013, vol. 66, no 4, pp. 548–599.

    http://dx.doi.org/10.1002/cpa.21437
  • 48M. J. P. Cullen, W. Gangbo, G. Pisante.

    The semigeostrophic equations discretized in reference and dual variables, in: Arch. Ration. Mech. Anal., 2007, vol. 185, no 2, pp. 341–363.

    http://dx.doi.org/10.1007/s00205-006-0040-6
  • 49M. J. P. Cullen, J. Norbury, R. J. Purser.

    Generalised Lagrangian solutions for atmospheric and oceanic flows, in: SIAM J. Appl. Math., 1991, vol. 51, no 1, pp. 20–31.

    http://dx.doi.org/10.1137/0151002
  • 50M. J. P. Cullen, R. J. Purser.

    An extended Lagrangian theory of semigeostrophic frontogenesis, in: J. Atmospheric Sci., 1984, vol. 41, no 9, pp. 1477–1497. [ DOI : 10.1175/1520-0469(1984)041<1477:AELTOS>2.0.CO;2 ]
  • 51B. Engquist, B. D. Froese.

    Application of the Wasserstein metric to seismic signals, 2013, Preprint.
  • 52A. Figalli, R. J. McCann, Y. Kim.

    When is multi-dimensional screening a convex program?, in: Journal of Economic Theory, 2011.
  • 53M. 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.
  • 54U. Frisch, S. Matarrese, R. Mohayaee, A. Sobolevskii.

    Monge-Ampère-Kantorovitch (MAK) reconstruction of the eary universe, in: Nature, 2002, vol. 417, no 260.
  • 55B. D. Froese, A. 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, no 4, pp. 1692–1714.

    http://dx.doi.org/10.1137/100803092
  • 56A. 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.
  • 57A. Galichon, B. Salanié.

    Matchings with Trade-Offs: Revealed preferences over Competing Characteristics, 2010, preprint.
  • 58A. Galichon, B. Salanié.

    Cupid's invisible hand: Social Surplus and Identification in Matching Models, 2011, preprint.
  • 59W. Gangbo, A. Świȩch.

    Optimal maps for the multidimensional Monge-Kantorovich problem, in: Comm. Pure Appl. Math., 1998, vol. 51, no 1, pp. 23–45, DOI : 10.1002/(SICI)1097-0312(199801)51:1<23::AID-CPA2>3.0.CO;2-H.
  • 60C. 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
  • 61B. J. Hoskins.

    The mathematical theory of frontogenesis, in: Annual review of fluid mechanics, Vol. 14, Palo Alto, CA, Annual Reviews, 1982, pp. 131–151.
  • 62R. Jordan, D. Kinderlehrer, F. Otto.

    The variational formulation of the Fokker-Planck equation, in: SIAM J. Math. Anal., 1998, vol. 29, no 1, pp. 1–17.

    http://dx.doi.org/10.1137/S0036141096303359
  • 63W. Jäger, S. Luckhaus.

    On explosions of solutions to a system of partial differential equations modelling chemotaxis, in: Trans. Amer. Math. Soc., 1992, vol. 329, no 2, pp. 819–824.

    http://dx.doi.org/10.2307/2153966
  • 64L. Kantorovitch.

    On the translocation of masses, in: C. R. (Doklady) Acad. Sci. URSS (N.S.), 1942, vol. 37, pp. 199–201.
  • 65J.-M. Lasry, P.-L. Lions.

    Mean field games, in: Jpn. J. Math., 2007, vol. 2, no 1, pp. 229–260.

    http://dx.doi.org/10.1007/s11537-007-0657-8
  • 66B. 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.
  • 67G. Loeper.

    A fully nonlinear version of the incompressible Euler equations: the semigeostrophic system, in: SIAM J. Math. Anal., 2006, vol. 38, no 3, pp. 795–823.

    http://dx.doi.org/10.1137/050629070
  • 68X.-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, no 2, pp. 151–183.

    http://dx.doi.org/10.1007/s00205-005-0362-9
  • 69B. Maury, A. Roudneff-Chupin, F. Santambrogio.

    A macroscopic crowd motion model of gradient flow type, in: Math. Models Methods Appl. Sci., 2010, vol. 20, no 10, pp. 1787–1821.

    http://dx.doi.org/10.1142/S0218202510004799
  • 70J.-M. Mirebeau.

    Adaptive, Anisotropic and Hierarchical cones of Discrete Convex functions, in: Preprint, 2014.
  • 71Q. Mérigot.

    A multiscale approach to optimal transport, in: Computer Graphics Forum, 2011, vol. 30, no 5, pp. 1583–1592.
  • 72Q. Mérigot.

    A Comparison of Two Dual Methods for Discrete Optimal Transport, in: Geometric Science of Information, Springer Berlin Heidelberg, 2013, pp. 389–396.
  • 73J. Nieto, F. Poupaud, J. Soler.

    High-field limit for the Vlasov-Poisson-Fokker-Planck system, in: Arch. Ration. Mech. Anal., 2001, vol. 158, no 1, pp. 29–59.

    http://dx.doi.org/10.1007/s002050100139
  • 74V. I. Oliker, L. D. Prussner.

    On the numerical solution of the equation (∂2z/∂x2)(∂2z/∂y2)-((∂2z/∂x∂y))2=f and its discretizations. I, in: Numer. Math., 1988, vol. 54, no 3, pp. 271–293.

    http://dx.doi.org/10.1007/BF01396762
  • 75N. Papadakis, G. Peyré, E. Oudet.

    Optimal Transport with Proximal Splitting, 2013, Preprint.
  • 76B. Pass.

    Convexity and multi-dimensional screening for spaces with different dimensions, in: J. Econom. Theory, 2012, vol. 147, no 6, pp. 2399–2418.

    http://dx.doi.org/10.1016/j.jet.2012.05.004
  • 77B. Pass.

    On the local structure of optimal measures in the multi-marginal optimal transportation problem, in: Calc. Var. Partial Differential Equations, 2012, vol. 43, no 3-4, pp. 529–536.

    http://dx.doi.org/10.1007/s00526-011-0421-z
  • 78B. Pass.

    On a Class of Optimal Transportation Problems with Infinitely Many Marginals, in: SIAM J. Math. Anal., 2013, vol. 45, no 4, pp. 2557–2575.

    http://dx.doi.org/10.1137/120881427
  • 79B. Pass.

    Optimal transportation with infinitely many marginals, in: J. Funct. Anal., 2013, vol. 264, no 4, pp. 947–963.

    http://dx.doi.org/10.1016/j.jfa.2012.12.002
  • 80A. 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.
  • 81C. 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
  • 82J. 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/
  • 83B. Salanié.

    The Economics of Contracts: a Primer, MIT Press, 1997.
  • 84C. 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
  • 85X.-J. Wang.

    On the design of a reflector antenna. II, in: Calc. Var. Partial Differential Equations, 2004, vol. 20, no 3, pp. 329–341.

    http://dx.doi.org/10.1007/s00526-003-0239-4
  • 86L. 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, no 6, pp. 1481–1495.

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


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