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MOKAPLAN - 2018
MOKAPLAN - 2018
Project-Team Mokaplan
Team, Visitors, External Collaborators
Overall Objectives
Research Program
Highlights of the Year
New Software and Platforms
New Results
Partnerships and Cooperations
Dissemination
Bibliography
Project-Team Mokaplan
Team, Visitors, External Collaborators
Overall Objectives
Research Program
Highlights of the Year
New Software and Platforms
New Results
Partnerships and Cooperations
Dissemination
Bibliography


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Bibliography

Major publications by the team in recent years
  • 1M. Agueh, G. Carlier.

    Barycenters in the Wasserstein space, in: SIAM J. Math. Anal., 2011, vol. 43, no 2, pp. 904–924.
  • 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, G. Carlier, M. Cuturi, L. Nenna, G. Peyré.

    Iterative Bregman Projections for Regularized Transportation Problems, in: SIAM Journal on Scientific Computing, 2015, vol. 37, no 2, pp. A1111-A1138. [ DOI : 10.1137/141000439 ]

    http://hal.archives-ouvertes.fr/hal-01096124
  • 4J.-D. Benamou, F. Collino, J.-M. Mirebeau.

    Monotone and Consistent discretization of the Monge-Ampere operator, September 2014, pubished in MAth of Comp.

    https://hal.archives-ouvertes.fr/hal-01067540
  • 5M. Bruveris, F.-X. Vialard.

    On Completeness of Groups of Diffeomorphisms, in: ArXiv e-prints, March 2014.
  • 6V. Duval, G. Peyré.

    Exact Support Recovery for Sparse Spikes Deconvolution, in: Foundations of Computational Mathematics, 2014, pp. 1-41.

    http://dx.doi.org/10.1007/s10208-014-9228-6
  • 7F. Gay-Balmaz, D. D. Holm, D. M. Meier, T. S. Ratiu, F.-X. Vialard.

    Invariant Higher-Order Variational Problems, in: Communications in Mathematical Physics, January 2012, vol. 309, pp. 413-458.

    http://dx.doi.org/10.1007/s00220-011-1313-y
  • 8P. Machado Manhães De Castro, Q. Mérigot, B. Thibert.

    Intersection of paraboloids and application to Minkowski-type problems, in: Numerische Mathematik, November 2015. [ DOI : 10.1007/s00211-015-0780-z ]

    https://hal.archives-ouvertes.fr/hal-00952720
  • 9Q. Mérigot.

    A multiscale approach to optimal transport, in: Computer Graphics Forum, 2011, vol. 30, no 5, pp. 1583–1592.
  • 10I. Waldspurger, A. Waters.

    Rank optimality for the Burer-Monteiro factorization, December 2018, preprint.

    https://hal.archives-ouvertes.fr/hal-01958814
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

Conferences without Proceedings

  • 24J.-B. Courbot, E. Monfrini, V. Mazet, C. Collet.

    Triplet markov trees for image segmentation, in: 2018 IEEE Workshop on Statistical Signal Processing (SSP 2018), Fribourg-en-Brisgau, Germany, June 2018.

    https://hal.archives-ouvertes.fr/hal-01815562
  • 25J. M. Fadili, G. Garrigos, J. Malick, G. Peyré.

    Model Consistency for Learning with Mirror-Stratifiable Regularizers, in: International Conference on Artificial Intelligence and Statistics (AISTATS), Naha, Japan, April 2019.

    https://hal.archives-ouvertes.fr/hal-01988309

Other Publications

References in notes
  • 40I. Abraham, R. Abraham, M. Bergounioux, G. Carlier.

    Tomographic reconstruction from a few views: a multi-marginal optimal transport approach, in: Preprint Hal-01065981, 2014.
  • 41Y. Achdou, V. Perez.

    Iterative strategies for solving linearized discrete mean field games systems, in: Netw. Heterog. Media, 2012, vol. 7, no 2, pp. 197–217.

    http://dx.doi.org/10.3934/nhm.2012.7.197
  • 42M. Agueh, G. Carlier.

    Barycenters in the Wasserstein space, in: SIAM J. Math. Anal., 2011, vol. 43, no 2, pp. 904–924.
  • 43F. Alter, V. Caselles, A. Chambolle.

    Evolution of Convex Sets in the Plane by Minimizing the Total Variation Flow, in: Interfaces and Free Boundaries, 2005, vol. 332, pp. 329–366.
  • 44F. R. Bach.

    Consistency of the Group Lasso and Multiple Kernel Learning, in: J. Mach. Learn. Res., June 2008, vol. 9, pp. 1179–1225.

    http://dl.acm.org/citation.cfm?id=1390681.1390721
  • 45F. R. Bach.

    Consistency of Trace Norm Minimization, in: J. Mach. Learn. Res., June 2008, vol. 9, pp. 1019–1048.

    http://dl.acm.org/citation.cfm?id=1390681.1390716
  • 46H. H. Bauschke, P. L. Combettes.

    A Dykstra-like algorithm for two monotone operators, in: Pacific Journal of Optimization, 2008, vol. 4, no 3, pp. 383–391.
  • 47M. F. Beg, M. I. Miller, A. Trouvé, L. Younes.

    Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms, in: International Journal of Computer Vision, February 2005, vol. 61, no 2, pp. 139–157.

    http://dx.doi.org/10.1023/B:VISI.0000043755.93987.aa
  • 48M. Beiglbock, P. Henry-Labordère, F. Penkner.

    Model-independent bounds for option prices mass transport approach, in: Finance and Stochastics, 2013, vol. 17, no 3, pp. 477-501.

    http://dx.doi.org/10.1007/s00780-013-0205-8
  • 49G. Bellettini, V. Caselles, M. Novaga.

    The Total Variation Flow in RN, in: J. Differential Equations, 2002, vol. 184, no 2, pp. 475–525.
  • 50J.-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
  • 51J.-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.
  • 52J.-D. Benamou, G. Carlier.

    Augmented Lagrangian algorithms for variational problems with divergence constraints, in: JOTA, 2015.
  • 53J.-D. Benamou, G. Carlier, N. Bonne.

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

    http://hal.inria.fr/hal-00922349
  • 54J.-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyré.

    Iterative Bregman Projections for Regularized Transportation Problems, in: SIAM J. Sci. Comp., 2015, to appear.
  • 55J.-D. Benamou, G. Carlier, M. Laborde.

    An augmented Lagrangian approach to Wasserstein gradient flows and applications, in: ESAIM: Proceedings and Surveys, August 2019.

    https://hal.archives-ouvertes.fr/hal-01245184
  • 56J.-D. Benamou, G. Carlier, Q. Mérigot, É. Oudet.

    Discretization of functionals involving the Monge-Ampère operator, HAL, July 2014.

    https://hal.archives-ouvertes.fr/hal-01056452
  • 57J.-D. Benamou, F. Collino, J.-M. Mirebeau.

    Monotone and Consistent discretization of the Monge-Ampère operator, in: arXiv preprint arXiv:1409.6694, 2014, to appear in Math of Comp.
  • 58J.-D. Benamou, B. D. Froese, A. Oberman.

    Two numerical methods for the elliptic Monge-Ampère equation, in: M2AN Math. Model. Numer. Anal., 2010, vol. 44, no 4, pp. 737–758.
  • 59J.-D. Benamou, B. D. Froese, A. Oberman.

    Numerical solution of the optimal transportation problem using the Monge–Ampere equation, in: Journal of Computational Physics, 2014, vol. 260, pp. 107–126.
  • 60F. 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.
  • 61M. Benning, M. Burger.

    Ground states and singular vectors of convex variational regularization methods, in: Meth. Appl. Analysis, 2013, vol. 20, pp. 295–334.
  • 62B. Berkels, A. Effland, M. Rumpf.

    Time discrete geodesic paths in the space of images, in: Arxiv preprint, 2014.
  • 63J. Bigot, T. Klein.

    Consistent estimation of a population barycenter in the Wasserstein space, in: Preprint arXiv:1212.2562, 2012.
  • 64A. Blanchet, P. Laurençot.

    The parabolic-parabolic Keller-Segel system with critical diffusion as a gradient flow in Rd,d≥3, in: Comm. Partial Differential Equations, 2013, vol. 38, no 4, pp. 658–686.

    http://dx.doi.org/10.1080/03605302.2012.757705
  • 65J. Bleyer, G. Carlier, V. Duval, J.-M. Mirebeau, G. Peyré.

    A Γ Convergence Result for the Upper Bound Limit Analysis of Plates, in: ESAIM: Mathematical Modelling and Numerical Analysis, January 2016, vol. 50, no 1, pp. 215–235. [ DOI : 10.1051/m2an/2015040 ]

    https://www.esaim-m2an.org/articles/m2an/abs/2016/01/m2an141087/m2an141087.html
  • 66N. Bonneel, J. Rabin, G. Peyré, H. Pfister.

    Sliced and Radon Wasserstein Barycenters of Measures, in: Journal of Mathematical Imaging and Vision, 2015, vol. 51, no 1, pp. 22–45.

    http://hal.archives-ouvertes.fr/hal-00881872/
  • 67U. Boscain, R. Chertovskih, J.-P. Gauthier, D. Prandi, A. Remizov.

    Highly corrupted image inpainting through hypoelliptic diffusion, Preprint CMAP, 2014.

    http://hal.archives-ouvertes.fr/hal-00842603/
  • 68G. Bouchitté, G. Buttazzo.

    Characterization of optimal shapes and masses through Monge-Kantorovich equation, in: J. Eur. Math. Soc. (JEMS), 2001, vol. 3, no 2, pp. 139–168.

    http://dx.doi.org/10.1007/s100970000027
  • 69N. Boumal, V. Voroninski, A. S. Bandeira.

    Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs, in: preprint, 2018, https://arxiv.org/abs/1804.02008.
  • 70L. Brasco, G. Carlier, F. Santambrogio.

    Congested traffic dynamics, weak flows and very degenerate elliptic equations, in: J. Math. Pures Appl. (9), 2010, vol. 93, no 6, pp. 652–671.
  • 71L. M. Bregman.

    The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, in: USSR computational mathematics and mathematical physics, 1967, vol. 7, no 3, pp. 200–217.
  • 72Y. Brenier.

    Generalized solutions and hydrostatic approximation of the Euler equations, in: Phys. D, 2008, vol. 237, no 14-17, pp. 1982–1988.

    http://dx.doi.org/10.1016/j.physd.2008.02.026
  • 73Y. 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.
  • 74Y. 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
  • 75Y. Brenier, U. Frisch, M. Henon, G. Loeper, S. Matarrese, R. Mohayaee, A. Sobolevski.

    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
  • 76M. Bruveris, L. Risser, F.-X. Vialard.

    Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups, in: Multiscale Modeling & Simulation, 2012, vol. 10, no 4, pp. 1344-1368.
  • 77S. Burer, R. D. C. Monteiro.

    A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization, in: Mathematical Programming, 2003, vol. 95, no 2, pp. 329-357.
  • 78M. Burger, M. Di Francesco, P. Markowich, M. T. Wolfram.

    Mean field games with nonlinear mobilities in pedestrian dynamics, in: DCDS B, 2014, vol. 19.
  • 79M. Burger, M. Franek, C.-B. Schönlieb.

    Regularized regression and density estimation based on optimal transport, in: Appl. Math. Res. Expr., 2012, vol. 2, pp. 209–253.
  • 80M. Burger, S. Osher.

    A guide to the TV zoo, in: Level-Set and PDE-based Reconstruction Methods, Springer, 2013.
  • 81G. Buttazzo, C. Jimenez, É. Oudet.

    An optimization problem for mass transportation with congested dynamics, in: SIAM J. Control Optim., 2009, vol. 48, no 3, pp. 1961–1976.
  • 82H. Byrne, D. Drasdo.

    Individual-based and continuum models of growing cell populations: a comparison, in: Journal of Mathematical Biology, 2009, vol. 58, no 4-5, pp. 657-687.
  • 83L. 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
  • 84L. A. Caffarelli, S. A. Kochengin, V. 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
  • 85C. Cancès, T. Gallouët, L. Monsaingeon.

    Incompressible immiscible multiphase flows in porous media: a variational approach, in: Analysis & PDE, 2017, vol. 10, no 8, pp. 1845–1876. [ DOI : 10.2140/apde.2017.10.1845 ]

    https://hal.archives-ouvertes.fr/hal-01345438
  • 86E. J. Candès, C. Fernandez-Granda.

    Super-Resolution from Noisy Data, in: Journal of Fourier Analysis and Applications, 2013, vol. 19, no 6, pp. 1229–1254.
  • 87E. J. Candès, C. Fernandez-Granda.

    Towards a Mathematical Theory of Super-Resolution, in: Communications on Pure and Applied Mathematics, 2014, vol. 67, no 6, pp. 906–956.
  • 88E. J. Candès, M. Wakin.

    An Introduction to Compressive Sensing, in: IEEE Signal Processing Magazine, 2008, vol. 25, no 2, pp. 21–30.
  • 89P. Cardaliaguet, G. Carlier, B. Nazaret.

    Geodesics for a class of distances in the space of probability measures, in: Calc. Var. Partial Differential Equations, 2013, vol. 48, no 3-4, pp. 395–420.
  • 90G. 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.
  • 91G. Carlier, V. Chernozhukov, A. Galichon.

    Vector Quantile Regression, Arxiv 1406.4643, 2014.
  • 92G. Carlier, M. Comte, I. Ionescu, G. Peyré.

    A Projection Approach to the Numerical Analysis of Limit Load Problems, in: Mathematical Models and Methods in Applied Sciences, 2011, vol. 21, no 6, pp. 1291–1316. [ DOI : doi:10.1142/S0218202511005325 ]

    http://hal.archives-ouvertes.fr/hal-00450000/
  • 93G. Carlier, X. Dupuis.

    An iterated projection approach to variational problems under generalized convexity constraints and applications, In preparation, 2015.
  • 94G. Carlier, C. Jimenez, F. Santambrogio.

    Optimal Transportation with Traffic Congestion and Wardrop Equilibria, in: SIAM Journal on Control and Optimization, 2008, vol. 47, no 3, pp. 1330-1350.
  • 95G. Carlier, T. Lachand-Robert, B. Maury.

    A numerical approach to variational problems subject to convexity constraint, in: Numer. Math., 2001, vol. 88, no 2, pp. 299–318.

    http://dx.doi.org/10.1007/PL00005446
  • 96G. Carlier, A. Oberman, É. Oudet.

    Numerical methods for matching for teams and Wasserstein barycenters, in: M2AN, 2015, to appear.
  • 97J. A. Carrillo, S. Lisini, E. Mainini.

    Uniqueness for Keller-Segel-type chemotaxis models, in: Discrete Contin. Dyn. Syst., 2014, vol. 34, no 4, pp. 1319–1338.

    http://dx.doi.org/10.3934/dcds.2014.34.1319
  • 98V. Caselles, A. Chambolle, M. Novaga.

    The discontinuity set of solutions of the TV denoising problem and some extensions, in: Multiscale Modeling and Simulation, 2007, vol. 6, no 3, pp. 879–894.
  • 99C. Ceritoglu, e. al..

    Computational Analysis of LDDMM for Brain Mapping, in: Frontiers in Neuroscience, 2013, vol. 7.
  • 100F. 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
  • 101A. Chambolle, T. Pock.

    On the ergodic convergence rates of a first-order primal-dual algorithm, in: Preprint OO/2014/09/4532, 2014.
  • 102G. Charpiat, G. Nardi, G. Peyré, F.-X. Vialard.

    Finsler Steepest Descent with Applications to Piecewise-regular Curve Evolution, Preprint hal-00849885, 2013.

    http://hal.archives-ouvertes.fr/hal-00849885/
  • 103S. S. Chen, D. L. Donoho, M. A. Saunders.

    Atomic decomposition by basis pursuit, in: SIAM journal on scientific computing, 1999, vol. 20, no 1, pp. 33–61.
  • 104P. Choné, H. V. J. Le Meur.

    Non-convergence result for conformal approximation of variational problems subject to a convexity constraint, in: Numer. Funct. Anal. Optim., 2001, vol. 22, no 5-6, pp. 529–547.

    http://dx.doi.org/10.1081/NFA-100105306
  • 105C. 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
  • 106M. 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
  • 107M. 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.
  • 108M. Cuturi.

    Sinkhorn Distances: Lightspeed Computation of Optimal Transport, in: Proc. NIPS, C. J. C. Burges, L. Bottou, Z. Ghahramani, K. Q. Weinberger (editors), 2013, pp. 2292–2300.
  • 109E. J. Dean, R. Glowinski.

    Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type, in: Comput. Methods Appl. Mech. Engrg., 2006, vol. 195, no 13-16, pp. 1344–1386.
  • 110V. Duval, G. Peyré.

    Exact Support Recovery for Sparse Spikes Deconvolution, in: Foundations of Computational Mathematics, 2014, pp. 1-41.

    http://dx.doi.org/10.1007/s10208-014-9228-6
  • 111V. Duval, G. Peyré.

    Sparse regularization on thin grids I: the L asso, in: Inverse Problems, 2017, vol. 33, no 5, 055008 p. [ DOI : 10.1088/1361-6420/aa5e12 ]

    http://stacks.iop.org/0266-5611/33/i=5/a=055008
  • 112J. Fehrenbach, J.-M. Mirebeau.

    Sparse Non-negative Stencils for Anisotropic Diffusion, in: Journal of Mathematical Imaging and Vision, 2014, vol. 49, no 1, pp. 123-147.

    http://dx.doi.org/10.1007/s10851-013-0446-3
  • 113C. Fernandez-Granda.

    Support detection in super-resolution, in: Proc. Proceedings of the 10th International Conference on Sampling Theory and Applications, 2013, pp. 145–148.
  • 114A. Figalli, R. McCann, Y. Kim.

    When is multi-dimensional screening a convex program?, in: Journal of Economic Theory, 2011.
  • 115J.-B. Fiot, H. Raguet, L. Risser, L. D. Cohen, J. Fripp, F.-X. Vialard.

    Longitudinal deformation models, spatial regularizations and learning strategies to quantify Alzheimer's disease progression, in: NeuroImage: Clinical, 2014, vol. 4, no 0, pp. 718 - 729. [ DOI : 10.1016/j.nicl.2014.02.002 ]

    http://www.sciencedirect.com/science/article/pii/S2213158214000205
  • 116J.-B. Fiot, L. Risser, L. D. Cohen, J. Fripp, F.-X. Vialard.

    Local vs Global Descriptors of Hippocampus Shape Evolution for Alzheimer's Longitudinal Population Analysis, in: Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data, Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2012, vol. 7570, pp. 13-24.

    http://dx.doi.org/10.1007/978-3-642-33555-6_2
  • 117U. Frisch, S. Matarrese, R. Mohayaee, A. Sobolevski.

    Monge-Ampère-Kantorovitch (MAK) reconstruction of the eary universe, in: Nature, 2002, vol. 417, no 260.
  • 118B. D. Froese, A. Oberman.

    Convergent filtered schemes for the Monge-Ampère partial differential equation, in: SIAM J. Numer. Anal., 2013, vol. 51, no 1, pp. 423–444.
  • 119A. Galichon, P. Henry-Labordère, N. Touzi.

    A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Loopback options, in: submitted to Annals of Applied Probability, 2011.
  • 120W. Gangbo, R. McCann.

    The geometry of optimal transportation, in: Acta Math., 1996, vol. 177, no 2, pp. 113–161.

    http://dx.doi.org/10.1007/BF02392620
  • 121E. Ghys.

    Gaspard Monge, Le mémoire sur les déblais et les remblais, in: Image des mathématiques, CNRS, 2012.

    http://images.math.cnrs.fr/Gaspard-Monge,1094.html
  • 122O. Guéant, J.-M. Lasry, P.-L. Lions.

    Mean field games and applications, in: Paris-Princeton Lectures on Mathematical Finance 2010, Berlin, Lecture Notes in Math., Springer, 2011, vol. 2003, pp. 205–266.

    http://dx.doi.org/10.1007/978-3-642-14660-2_3
  • 123G. Herman.

    Image reconstruction from projections: the fundamentals of computerized tomography, Academic Press, 1980.
  • 124D. D. Holm, J. T. Ratnanather, A. Trouvé, L. Younes.

    Soliton dynamics in computational anatomy, in: NeuroImage, 2004, vol. 23, pp. S170–S178.
  • 125B. J. Hoskins.

    The mathematical theory of frontogenesis, in: Annual review of fluid mechanics, Vol. 14, Palo Alto, CA, Annual Reviews, 1982, pp. 131–151.
  • 126R. 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.
  • 127W. 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
  • 128L. Kantorovitch.

    On the translocation of masses, in: C. R. (Doklady) Acad. Sci. URSS (N.S.), 1942, vol. 37, pp. 199–201.
  • 129E. Klann.

    A Mumford-Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography, in: SIAM J. Imaging Sciences, 2011, vol. 4, no 4, pp. 1029–1048.
  • 130J.-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
  • 131J. Lasserre.

    Global Optimization with Polynomials and the Problem of Moments, in: SIAM Journal on Optimization, 2001, vol. 11, no 3, pp. 796-817.
  • 132J. Lellmann, D. A. Lorenz, C. Schönlieb, T. Valkonen.

    Imaging with Kantorovich-Rubinstein Discrepancy, in: SIAM J. Imaging Sciences, 2014, vol. 7, no 4, pp. 2833–2859.
  • 133A. S. Lewis.

    Active sets, nonsmoothness, and sensitivity, in: SIAM Journal on Optimization, 2003, vol. 13, no 3, pp. 702–725.
  • 134B. Li, F. Habbal, M. Ortiz.

    Optimal transportation meshfree approximation schemes for Fluid and plastic Flows, in: Int. J. Numer. Meth. Engng 83:1541–579, 2010, vol. 83, pp. 1541–1579.
  • 135G. 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 (electronic).
  • 136G. Loeper, F. Rapetti.

    Numerical solution of the Monge-Ampére equation by a Newton's algorithm, in: C. R. Math. Acad. Sci. Paris, 2005, vol. 340, no 4, pp. 319–324.
  • 137D. Lombardi, E. Maitre.

    Eulerian models and algorithms for unbalanced optimal transport, in: Preprint hal-00976501, 2013.
  • 138C. Léonard.

    A survey of the Schrödinger problem and some of its connections with optimal transport, in: Discrete Contin. Dyn. Syst., 2014, vol. 34, no 4, pp. 1533–1574.

    http://dx.doi.org/10.3934/dcds.2014.34.1533
  • 139J. Maas, M. Rumpf, C.-B. Schönlieb, S. Simon.

    A generalized model for optimal transport of images including dissipation and density modulation, in: Arxiv preprint, 2014.
  • 140S. G. Mallat.

    A wavelet tour of signal processing, Third, Elsevier/Academic Press, Amsterdam, 2009.
  • 141B. 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
  • 142M. I. Miller, A. Trouvé, L. Younes.

    Geodesic Shooting for Computational Anatomy, in: Journal of Mathematical Imaging and Vision, March 2006, vol. 24, no 2, pp. 209–228.

    http://dx.doi.org/10.1007/s10851-005-3624-0
  • 143J.-M. Mirebeau.

    Adaptive, Anisotropic and Hierarchical cones of Discrete Convex functions, in: Preprint, 2014.
  • 144J.-M. Mirebeau.

    Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction, in: SIAM Journal on Numerical Analysis, 2014, vol. 52, no 4, pp. 1573-1599.
  • 145Q. Mérigot.

    A multiscale approach to optimal transport, in: Computer Graphics Forum, 2011, vol. 30, no 5, pp. 1583–1592.
  • 146Q. Mérigot, É. Oudet.

    Handling Convexity-Like Constraints in Variational Problems, in: SIAM J. Numer. Anal., 2014, vol. 52, no 5, pp. 2466–2487.
  • 147N. Papadakis, G. Peyré, É. Oudet.

    Optimal Transport with Proximal Splitting, in: SIAM Journal on Imaging Sciences, 2014, vol. 7, no 1, pp. 212–238. [ DOI : 10.1137/130920058 ]

    http://hal.archives-ouvertes.fr/hal-00816211/
  • 148B. Pass, N. Ghoussoub.

    Optimal transport: From moving soil to same-sex marriage, in: CMS Notes, 2013, vol. 45, pp. 14–15.
  • 149B. Pass.

    Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem, in: SIAM Journal on Mathematical Analysis, 2011, vol. 43, no 6, pp. 2758-2775.
  • 150B. Perthame, F. Quiros, J. L. Vazquez.

    The Hele-Shaw Asymptotics for Mechanical Models of Tumor Growth, in: Archive for Rational Mechanics and Analysis, 2014, vol. 212, no 1, pp. 93-127.

    http://dx.doi.org/10.1007/s00205-013-0704-y
  • 151J. Petitot.

    The neurogeometry of pinwheels as a sub-riemannian contact structure, in: Journal of Physiology-Paris, 2003, vol. 97, no 23, pp. 265–309.
  • 152G. Peyré.

    Texture Synthesis with Grouplets, in: Pattern Analysis and Machine Intelligence, IEEE Transactions on, April 2010, vol. 32, no 4, pp. 733–746.
  • 153B. Piccoli, F. Rossi.

    Generalized Wasserstein distance and its application to transport equations with source, in: Archive for Rational Mechanics and Analysis, 2014, vol. 211, no 1, pp. 335–358.
  • 154C. Poon.

    Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames, in: Applied and Computational Harmonic Analysis, 2015.
  • 155H. Raguet, J. Fadili, G. Peyré.

    A Generalized Forward-Backward Splitting, in: SIAM Journal on Imaging Sciences, 2013, vol. 6, no 3, pp. 1199–1226. [ DOI : 10.1137/120872802 ]

    http://hal.archives-ouvertes.fr/hal-00613637/
  • 156J.-C. Rochet, P. Choné.

    Ironing, Sweeping and multi-dimensional screening, in: Econometrica, 1998.
  • 157L. Rudin, S. Osher, E. Fatemi.

    Nonlinear total variation based noise removal algorithms, in: Physica D: Nonlinear Phenomena, 1992, vol. 60, no 1, pp. 259–268.

    http://dx.doi.org/10.1016/0167-2789(92)90242-F
  • 158O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen.

    Variational Methods in Imaging, Springer, 2008.
  • 159T. Schmah, L. Risser, F.-X. Vialard.

    Left-Invariant Metrics for Diffeomorphic Image Registration with Spatially-Varying Regularisation, in: MICCAI (1), 2013, pp. 203-210.
  • 160T. Schmah, L. Risser, F.-X. Vialard.

    Diffeomorphic image matching with left-invariant metrics, in: Fields Institute Communications series, special volume in memory of Jerrold E. Marsden, January 2014.
  • 161J. Solomon, F. de Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, L. Guibas.

    Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains, in: ACM Transaction on Graphics, Proc. SIGGRAPH'15, 2015, to appear.
  • 162R. Tibshirani.

    Regression shrinkage and selection via the Lasso, in: Journal of the Royal Statistical Society. Series B. Methodological, 1996, vol. 58, no 1, pp. 267–288.
  • 163A. Trouvé, F.-X. Vialard.

    Shape splines and stochastic shape evolutions: A second order point of view, in: Quarterly of Applied Mathematics, 2012.
  • 164S. Vaiter, M. Golbabaee, J. Fadili, G. Peyré.

    Model Selection with Piecewise Regular Gauges, in: Information and Inference, 2015, to appear.

    http://hal.archives-ouvertes.fr/hal-00842603/
  • 165F.-X. Vialard, L. Risser, D. Rueckert, C. Cotter.

    Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation, in: International Journal of Computer Vision, 2012, vol. 97, no 2, pp. 229-241.

    http://dx.doi.org/10.1007/s11263-011-0481-8
  • 166F.-X. Vialard, L. Risser.

    Spatially-Varying Metric Learning for Diffeomorphic Image Registration: A Variational Framework, in: Medical Image Computing and Computer-Assisted Intervention MICCAI 2014, Lecture Notes in Computer Science, Springer International Publishing, 2014, vol. 8673, pp. 227-234.
  • 167C. Villani.

    Topics in optimal transportation, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2003, vol. 58, xvi+370 p.
  • 168C. 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
  • 169X.-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
  • 170B. Wirth, L. Bar, M. Rumpf, G. Sapiro.

    A continuum mechanical approach to geodesics in shape space, in: International Journal of Computer Vision, 2011, vol. 93, no 3, pp. 293–318.
  • 171J. Wright, Y. Ma, J. Mairal, G. Sapiro, T. S. Huang, S. Yan.

    Sparse representation for computer vision and pattern recognition, in: Proceedings of the IEEE, 2010, vol. 98, no 6, pp. 1031–1044.


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