Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 1A. Genevay.
  
  Entropy-Regularized Optimal Transport for Machine Learning, PSL University, March 2019.
  
  https://tel.archives-ouvertes.fr/tel-02319318

Articles in International Peer-Reviewed Journals

• 2J.-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
• 3J.-D. Benamou, V. Duval.
  
  Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem, in: European Journal of Applied Mathematics, 2019, https://arxiv.org/abs/1710.05594, forthcoming. [ DOI : 10.1017/S0956792518000451 ]
  
  https://hal.inria.fr/hal-01616842
• 4J.-D. Benamou, T. Gallouët, F.-X. Vialard.
  
  Second order models for optimal transport and cubic splines on the Wasserstein space, in: Foundations of Computational Mathematics, October 2019, https://arxiv.org/abs/1801.04144.
  
  https://hal.archives-ouvertes.fr/hal-01682107
• 5C. Boyer, A. Chambolle, Y. De Castro, V. Duval, F. De Gournay, P. Weiss.
  
  On Representer Theorems and Convex Regularization, in: SIAM Journal on Optimization, May 2019, vol. 29, n^o 2, pp. 1260–1281, https://arxiv.org/abs/1806.09810. [ DOI : 10.1137/18M1200750 ]
  
  https://hal.archives-ouvertes.fr/hal-01823135
• 6C. Cancès, T. Gallouët, M. Laborde, L. Monsaingeon.
  
  Simulation of multiphase porous media flows with minimizing movement and finite volume schemes, in: European Journal of Applied Mathematics, 2019, vol. 30, n^o 6, pp. 1123-1152. [ DOI : 10.1017/S0956792518000633 ]
  
  https://hal.archives-ouvertes.fr/hal-01700952
• 7S. Dallaporta, Y. De Castro.
  
  Sparse Recovery from Extreme Eigenvalues Deviation Inequalities, in: ESAIM: Probability and Statistics, 2019, https://arxiv.org/abs/1604.01171 - 33 pages, 1 figure. [ DOI : 10.1051/ps/2018024 ]
  
  https://hal.archives-ouvertes.fr/hal-01309439
• 8Y. De Castro, F. Gamboa, D. Henrion, R. Hess, J. B. Lasserre.
  
  Approximate Optimal Designs for Multivariate Polynomial Regression, in: Annals of Statistics, January 2019, vol. 47, n^o 1, pp. 127-155. [ DOI : 10.1214/18-AOS1683 ]
  
  https://hal.laas.fr/hal-01483490
• 9Q. Denoyelle, V. Duval, G. Peyré, E. Soubies.
  
  The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy, in: Inverse Problems, 2019, https://arxiv.org/abs/1811.06416, forthcoming. [ DOI : 10.1088/1361-6420/ab2a29 ]
  
  https://hal.archives-ouvertes.fr/hal-01921604
• 10T. Gallouët, M. Laborde, L. Monsaingeon.
  
  An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems, in: ESAIM: Control, Optimisation and Calculus of Variations, 2019, vol. 25, n^o 8, https://arxiv.org/abs/1704.04541. [ DOI : 10.1051/cocv/2018001 ]
  
  https://hal.archives-ouvertes.fr/hal-01508911
• 11T. Gallouët, A. Natale, F.-X. Vialard.
  
  Generalized compressible flows and solutions of the H(div) geodesic problem, in: Archive for Rational Mechanics and Analysis, 2020, https://arxiv.org/abs/1806.10825, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-01815531
• 12R. E. Gaunt, G. Mijoule, Y. Swan.
  
  Some new Stein operators for product distributions, in: Brazilian Journal of Probability and Statistics, 2019, https://arxiv.org/abs/1901.11460 - 13 pages, forthcoming.
  
  https://hal.archives-ouvertes.fr/hal-02017801
• 13A. Natale, F.-X. Vialard.
  
  Embedding Camassa-Holm equations in incompressible Euler, in: Journal of Geometric Mechanics, June 2019, https://arxiv.org/abs/1804.11080.
  
  https://hal.archives-ouvertes.fr/hal-01781162
• 14P. Pegon, F. Santambrogio, Q. Xia.
  
  A fractal shape optimization problem in branched transport, in: Journal de Mathématiques Pures et Appliquées, March 2019, https://arxiv.org/abs/1709.01415.
  
  https://hal.archives-ouvertes.fr/hal-01581675

International Conferences with Proceedings

• 15J.-B. Courbot, E. Monfrini, V. Mazet, C. Collet.
  
  Triplet markov trees for image segmentation, in: SSP 2018: IEEE Workshop on Statistical Signal Processing, Fribourg-en-Brisgau, Germany, 2018 IEEE Statistical Signal Processing Workshop (SSP), IEEE Computer Society, 2019, pp. 233-237. [ DOI : 10.1109/SSP.2018.8450841 ]
  
  https://hal.archives-ouvertes.fr/hal-01815562

Conferences without Proceedings

• 16J. 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

• 17J.-M. Azaïs, Y. De Castro.
  
  Multiple Testing and Variable Selection along Least Angle Regression's path, July 2019, https://arxiv.org/abs/1906.12072 - 39 pages, 7 figures.
  
  https://hal.archives-ouvertes.fr/hal-02170476
• 18J.-D. Benamou, G. Carlier, S. D. Marino, L. Nenna.
  
  An entropy minimization approach to second-order variational mean-field games, September 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01848370
• 19C. Cancès, T. Gallouët, G. Todeschi.
  
  A variational finite volume scheme for Wasserstein gradient flows, July 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02189050
• 20J.-B. Courbot, V. Duval, B. Legras.
  
  Sparse analysis for mesoscale convective systems tracking, February 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02010436
• 21S. Di Marino, A. Natale, R. Tahraoui, F.-X. Vialard.
  
  Metric completion of $Diff\left(\right[0,1\left]\right)$ with the $H1$ right-invariant metric, June 2019, https://arxiv.org/abs/1906.09139 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02161686
• 22V. Duval.
  
  An Epigraphical Approach to the Representer Theorem, December 2019, https://arxiv.org/abs/1912.13224 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02424908
• 23G. Mijoule, G. Reinert, Y. Swan.
  
  Stein operators, kernels and discrepancies for multivariate continuous distributions, December 2019, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02420874
• 24A. Natale, G. Todeschi.
  
  TPFA Finite Volume Approximation of Wasserstein Gradient Flows, January 2020, https://arxiv.org/abs/2001.07005 - working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-02444833

References in notes

• 25I. Abraham, R. Abraham, M. Bergounioux, G. Carlier.
  
  Tomographic reconstruction from a few views: a multi-marginal optimal transport approach, in: Preprint Hal-01065981, 2014.
• 26Y. Achdou, V. Perez.
  
  Iterative strategies for solving linearized discrete mean field games systems, in: Netw. Heterog. Media, 2012, vol. 7, n^o 2, pp. 197–217.
  
  http://dx.doi.org/10.3934/nhm.2012.7.197
• 27M. Agueh, G. Carlier.
  
  Barycenters in the Wasserstein space, in: SIAM J. Math. Anal., 2011, vol. 43, n^o 2, pp. 904–924.
• 28F. 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.
• 29F. 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
• 30F. 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
• 31H. H. Bauschke, P. L. Combettes.
  
  A Dykstra-like algorithm for two monotone operators, in: Pacific Journal of Optimization, 2008, vol. 4, n^o 3, pp. 383–391.
• 32M. 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, n^o 2, pp. 139–157.
  
  http://dx.doi.org/10.1023/B:VISI.0000043755.93987.aa
• 33M. Beiglbock, P. Henry-Labordère, F. Penkner.
  
  Model-independent bounds for option prices mass transport approach, in: Finance and Stochastics, 2013, vol. 17, n^o 3, pp. 477-501.
  
  http://dx.doi.org/10.1007/s00780-013-0205-8
• 34G. Bellettini, V. Caselles, M. Novaga.
  
  The Total Variation Flow in $R^N$, in: J. Differential Equations, 2002, vol. 184, n^o 2, pp. 475–525.
• 35J.-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
• 36J.-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.
• 37J.-D. Benamou, G. Carlier.
  
  Augmented Lagrangian algorithms for variational problems with divergence constraints, in: JOTA, 2015.
• 38J.-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
• 39J.-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.
• 40J.-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
• 41J.-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.
• 42J.-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, n^o 4, pp. 737–758.
• 43J.-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.
• 44F. 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.
• 45M. Benning, M. Burger.
  
  Ground states and singular vectors of convex variational regularization methods, in: Meth. Appl. Analysis, 2013, vol. 20, pp. 295–334.
• 46B. Berkels, A. Effland, M. Rumpf.
  
  Time discrete geodesic paths in the space of images, in: Arxiv preprint, 2014.
• 47J. Bigot, T. Klein.
  
  Consistent estimation of a population barycenter in the Wasserstein space, in: Preprint arXiv:1212.2562, 2012.
• 48A. Blanchet, P. Laurençot.
  
  The parabolic-parabolic Keller-Segel system with critical diffusion as a gradient flow in $R^d,d\ge 3$, in: Comm. Partial Differential Equations, 2013, vol. 38, n^o 4, pp. 658–686.
  
  http://dx.doi.org/10.1080/03605302.2012.757705
• 49J. Bleyer, G. Carlier, V. Duval, J.-M. Mirebeau, G. Peyré.
  
  A $\Gamma$ Convergence Result for the Upper Bound Limit Analysis of Plates, in: ESAIM: Mathematical Modelling and Numerical Analysis, January 2016, vol. 50, n^o 1, pp. 215–235. [ DOI : 10.1051/m2an/2015040 ]
  
  https://www.esaim-m2an.org/articles/m2an/abs/2016/01/m2an141087/m2an141087.html
• 50N. Bonneel, J. Rabin, G. Peyré, H. Pfister.
  
  Sliced and Radon Wasserstein Barycenters of Measures, in: Journal of Mathematical Imaging and Vision, 2015, vol. 51, n^o 1, pp. 22–45.
  
  http://hal.archives-ouvertes.fr/hal-00881872/
• 51U. 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/
• 52G. Bouchitté, G. Buttazzo.
  
  Characterization of optimal shapes and masses through Monge-Kantorovich equation, in: J. Eur. Math. Soc. (JEMS), 2001, vol. 3, n^o 2, pp. 139–168.
  
  http://dx.doi.org/10.1007/s100970000027
• 53L. Brasco, G. Carlier, F. Santambrogio.
  
  Congested traffic dynamics, weak flows and very degenerate elliptic equations, in: J. Math. Pures Appl. (9), 2010, vol. 93, n^o 6, pp. 652–671.
• 54L. 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, n^o 3, pp. 200–217.
• 55Y. Brenier.
  
  Generalized solutions and hydrostatic approximation of the Euler equations, in: Phys. D, 2008, vol. 237, n^o 14-17, pp. 1982–1988.
  
  http://dx.doi.org/10.1016/j.physd.2008.02.026
• 56Y. 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.
• 57Y. 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
• 58Y. 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
• 59M. Bruveris, L. Risser, F.-X. Vialard.
  
  Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups, in: Multiscale Modeling & Simulation, 2012, vol. 10, n^o 4, pp. 1344-1368.
• 60M. Burger, M. DiFrancesco, P. Markowich, M. T. Wolfram.
  
  Mean field games with nonlinear mobilities in pedestrian dynamics, in: DCDS B, 2014, vol. 19.
• 61M. Burger, M. Franek, C. Schonlieb.
  
  Regularized regression and density estimation based on optimal transport, in: Appl. Math. Res. Expr., 2012, vol. 2, pp. 209–253.
• 62M. Burger, S. Osher.
  
  A guide to the TV zoo, in: Level-Set and PDE-based Reconstruction Methods, Springer, 2013.
• 63G. 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.
• 64H. Byrne, D. Drasdo.
  
  Individual-based and continuum models of growing cell populations: a comparison, in: Journal of Mathematical Biology, 2009, vol. 58, n^o 4-5, pp. 657-687.
• 65L. 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
• 66L. 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
• 67C. CanCeritoglu.
  
  Computational Analysis of LDDMM for Brain Mapping, in: Frontiers in Neuroscience, 2013, vol. 7.
• 68C. Cancès, T. Gallouët, L. Monsaingeon.
  
  Incompressible immiscible multiphase flows in porous media: a variational approach, in: Analysis & PDE, 2017, vol. 10, n^o 8, pp. 1845–1876. [ DOI : 10.2140/apde.2017.10.1845 ]
  
  https://hal.archives-ouvertes.fr/hal-01345438
• 69E. Candes, M. Wakin.
  
  An Introduction to Compressive Sensing, in: IEEE Signal Processing Magazine, 2008, vol. 25, n^o 2, pp. 21–30.
• 70E. J. Candès, C. Fernandez-Granda.
  
  Super-Resolution from Noisy Data, in: Journal of Fourier Analysis and Applications, 2013, vol. 19, n^o 6, pp. 1229–1254.
• 71E. J. Candès, C. Fernandez-Granda.
  
  Towards a Mathematical Theory of Super-Resolution, in: Communications on Pure and Applied Mathematics, 2014, vol. 67, n^o 6, pp. 906–956.
• 72P. 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, n^o 3-4, pp. 395–420.
• 73G. 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.
• 74G. Carlier, V. Chernozhukov, A. Galichon.
  
  Vector Quantile Regression, Arxiv 1406.4643, 2014.
• 75G. 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, n^o 6, pp. 1291–1316. [ DOI : doi:10.1142/S0218202511005325 ]
  
  http://hal.archives-ouvertes.fr/hal-00450000/
• 76G. Carlier, X. Dupuis.
  
  An iterated projection approach to variational problems under generalized convexity constraints and applications, In preparation, 2015.
• 77G. Carlier, C. Jimenez, F. Santambrogio.
  
  Optimal Transportation with Traffic Congestion and Wardrop Equilibria, in: SIAM Journal on Control and Optimization, 2008, vol. 47, n^o 3, pp. 1330-1350.
• 78G. Carlier, T. Lachand-Robert, B. Maury.
  
  A numerical approach to variational problems subject to convexity constraint, in: Numer. Math., 2001, vol. 88, n^o 2, pp. 299–318.
  
  http://dx.doi.org/10.1007/PL00005446
• 79G. Carlier, A. Oberman, É. Oudet.
  
  Numerical methods for matching for teams and Wasserstein barycenters, in: M2AN, 2015, to appear.
• 80J. A. Carrillo, S. Lisini, E. Mainini.
  
  Uniqueness for Keller-Segel-type chemotaxis models, in: Discrete Contin. Dyn. Syst., 2014, vol. 34, n^o 4, pp. 1319–1338.
  
  http://dx.doi.org/10.3934/dcds.2014.34.1319
• 81V. 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, n^o 3, pp. 879–894.
• 82F. 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
• 83A. Chambolle, T. Pock.
  
  On the ergodic convergence rates of a first-order primal-dual algorithm, in: Preprint OO/2014/09/4532, 2014.
• 84G. 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/
• 85S. S. Chen, D. L. Donoho, M. A. Saunders.
  
  Atomic decomposition by basis pursuit, in: SIAM journal on scientific computing, 1999, vol. 20, n^o 1, pp. 33–61.
• 86P. 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, n^o 5-6, pp. 529–547.
  
  http://dx.doi.org/10.1081/NFA-100105306
• 87C. Cotar, G. Friesecke, C. Kluppelberg.
  
  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
• 88M. 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
• 89M. 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.
• 90M. 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.
• 91E. 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, n^o 13-16, pp. 1344–1386.
• 92V. 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
• 93V. Duval, G. Peyré.
  
  Sparse regularization on thin grids I: the L asso, in: Inverse Problems, 2017, vol. 33, n^o 5, 055008 p. [ DOI : 10.1088/1361-6420/aa5e12 ]
  
  http://stacks.iop.org/0266-5611/33/i=5/a=055008
• 94J. Fehrenbach, J.-M. Mirebeau.
  
  Sparse Non-negative Stencils for Anisotropic Diffusion, in: Journal of Mathematical Imaging and Vision, 2014, vol. 49, n^o 1, pp. 123-147.
  
  http://dx.doi.org/10.1007/s10851-013-0446-3
• 95C. Fernandez-Granda.
  
  Support detection in super-resolution, in: Proc. Proceedings of the 10th International Conference on Sampling Theory and Applications, 2013, pp. 145–148.
• 96A. Figalli, R. McCann, Y. Kim.
  
  When is multi-dimensional screening a convex program?, in: Journal of Economic Theory, 2011.
• 97J.-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, n^o 0, pp. 718 - 729. [ DOI : 10.1016/j.nicl.2014.02.002 ]
  
  http://www.sciencedirect.com/science/article/pii/S2213158214000205
• 98J.-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
• 99U. Frisch, S. Matarrese, R. Mohayaee, A. Sobolevski.
  
  Monge-Ampère-Kantorovitch (MAK) reconstruction of the eary universe, in: Nature, 2002, vol. 417, n^o 260.
• 100B. D. Froese, A. Oberman.
  
  Convergent filtered schemes for the Monge-Ampère partial differential equation, in: SIAM J. Numer. Anal., 2013, vol. 51, n^o 1, pp. 423–444.
• 101A. 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.
• 102W. Gangbo, R. McCann.
  
  The geometry of optimal transportation, in: Acta Math., 1996, vol. 177, n^o 2, pp. 113–161.
  
  http://dx.doi.org/10.1007/BF02392620
• 103E. 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
• 104O. 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
• 105G. Herman.
  
  Image reconstruction from projections: the fundamentals of computerized tomography, Academic Press, 1980.
• 106D. D. Holm, J. T. Ratnanather, A. Trouvé, L. Younes.
  
  Soliton dynamics in computational anatomy, in: NeuroImage, 2004, vol. 23, pp. S170–S178.
• 107B. J. Hoskins.
  
  The mathematical theory of frontogenesis, in: Annual review of fluid mechanics, Vol. 14, Palo Alto, CA, Annual Reviews, 1982, pp. 131–151.
• 108R. 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.
• 109W. 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
• 110L. Kantorovitch.
  
  On the translocation of masses, in: C. R. (Doklady) Acad. Sci. URSS (N.S.), 1942, vol. 37, pp. 199–201.
• 111E. Klann.
  
  A Mumford-Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography, in: SIAM J. Imaging Sciences, 2011, vol. 4, n^o 4, pp. 1029–1048.
• 112J.-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
• 113J. Lasserre.
  
  Global Optimization with Polynomials and the Problem of Moments, in: SIAM Journal on Optimization, 2001, vol. 11, n^o 3, pp. 796-817.
• 114J. Lellmann, D. A. Lorenz, C. Schönlieb, T. Valkonen.
  
  Imaging with Kantorovich-Rubinstein Discrepancy, in: SIAM J. Imaging Sciences, 2014, vol. 7, n^o 4, pp. 2833–2859.
• 115A. S. Lewis.
  
  Active sets, nonsmoothness, and sensitivity, in: SIAM Journal on Optimization, 2003, vol. 13, n^o 3, pp. 702–725.
• 116B. 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.
• 117G. 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 (electronic).
• 118G. 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, n^o 4, pp. 319–324.
• 119D. Lombardi, E. Maitre.
  
  Eulerian models and algorithms for unbalanced optimal transport, in: Preprint hal-00976501, 2013.
• 120C. Léonard.
  
  A survey of the Schrödinger problem and some of its connections with optimal transport, in: Discrete Contin. Dyn. Syst., 2014, vol. 34, n^o 4, pp. 1533–1574.
  
  http://dx.doi.org/10.3934/dcds.2014.34.1533
• 121J. Maas, M. Rumpf, C. Schonlieb, S. Simon.
  
  A generalized model for optimal transport of images including dissipation and density modulation, in: Arxiv preprint, 2014.
• 122S. G. Mallat.
  
  A wavelet tour of signal processing, Third, Elsevier/Academic Press, Amsterdam, 2009.
• 123B. 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
• 124M. I. Miller, A. Trouvé, L. Younes.
  
  Geodesic Shooting for Computational Anatomy, in: Journal of Mathematical Imaging and Vision, March 2006, vol. 24, n^o 2, pp. 209–228.
  
  http://dx.doi.org/10.1007/s10851-005-3624-0
• 125J.-M. Mirebeau.
  
  Adaptive, Anisotropic and Hierarchical cones of Discrete Convex functions, in: Preprint, 2014.
• 126J.-M. Mirebeau.
  
  Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction, in: SIAM Journal on Numerical Analysis, 2014, vol. 52, n^o 4, pp. 1573-1599.
• 127Q. Mérigot.
  
  A multiscale approach to optimal transport, in: Computer Graphics Forum, 2011, vol. 30, n^o 5, pp. 1583–1592.
• 128Q. Mérigot, É. Oudet.
  
  Handling Convexity-Like Constraints in Variational Problems, in: SIAM J. Numer. Anal., 2014, vol. 52, n^o 5, pp. 2466–2487.
• 129N. Papadakis, G. Peyré, É. Oudet.
  
  Optimal Transport with Proximal Splitting, in: SIAM Journal on Imaging Sciences, 2014, vol. 7, n^o 1, pp. 212–238. [ DOI : 10.1137/130920058 ]
  
  http://hal.archives-ouvertes.fr/hal-00816211/
• 130B. Pass, N. Ghoussoub.
  
  Optimal transport: From moving soil to same-sex marriage, in: CMS Notes, 2013, vol. 45, pp. 14–15.
• 131B. Pass.
  
  Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem, in: SIAM Journal on Mathematical Analysis, 2011, vol. 43, n^o 6, pp. 2758-2775.
• 132B. 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, n^o 1, pp. 93-127.
  
  http://dx.doi.org/10.1007/s00205-013-0704-y
• 133J. Petitot.
  
  The neurogeometry of pinwheels as a sub-riemannian contact structure, in: Journal of Physiology-Paris, 2003, vol. 97, n^o 23, pp. 265–309.
• 134G. Peyré.
  
  Texture Synthesis with Grouplets, in: Pattern Analysis and Machine Intelligence, IEEE Transactions on, April 2010, vol. 32, n^o 4, pp. 733–746.
• 135B. Piccoli, F. Rossi.
  
  Generalized Wasserstein distance and its application to transport equations with source, in: Archive for Rational Mechanics and Analysis, 2014, vol. 211, n^o 1, pp. 335–358.
• 136C. Poon.
  
  Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames, in: Applied and Computational Harmonic Analysis, 2015.
• 137H. Raguet, J. Fadili, G. Peyré.
  
  A Generalized Forward-Backward Splitting, in: SIAM Journal on Imaging Sciences, 2013, vol. 6, n^o 3, pp. 1199–1226. [ DOI : 10.1137/120872802 ]
  
  http://hal.archives-ouvertes.fr/hal-00613637/
• 138J.-C. Rochet, P. Choné.
  
  Ironing, Sweeping and multi-dimensional screening, in: Econometrica, 1998.
• 139L. Rudin, S. Osher, E. Fatemi.
  
  Nonlinear total variation based noise removal algorithms, in: Physica D: Nonlinear Phenomena, 1992, vol. 60, n^o 1, pp. 259–268.
  
  http://dx.doi.org/10.1016/0167-2789(92)90242-F
• 140O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen.
  
  Variational Methods in Imaging, Springer, 2008.
• 141T. Schmah, L. Risser, F.-X. Vialard.
  
  Left-Invariant Metrics for Diffeomorphic Image Registration with Spatially-Varying Regularisation, in: MICCAI (1), 2013, pp. 203-210.
• 142T. 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.
• 143J. 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.
• 144R. Tibshirani.
  
  Regression shrinkage and selection via the Lasso, in: Journal of the Royal Statistical Society. Series B. Methodological, 1996, vol. 58, n^o 1, pp. 267–288.
• 145A. Trouvé, F.-X. Vialard.
  
  Shape splines and stochastic shape evolutions: A second order point of view, in: Quarterly of Applied Mathematics, 2012.
• 146S. 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/
• 147F.-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, n^o 2, pp. 229-241.
  
  http://dx.doi.org/10.1007/s11263-011-0481-8
• 148F.-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.
• 149C. Villani.
  
  Topics in optimal transportation, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2003, vol. 58, xvi+370 p.
• 150C. 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
• 151X.-J. Wang.
  
  On the design of a reflector antenna. II, in: Calc. Var. Partial Differential Equations, 2004, vol. 20, n^o 3, pp. 329–341.
  
  http://dx.doi.org/10.1007/s00526-003-0239-4
• 152B. 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, n^o 3, pp. 293–318.
• 153J. 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, n^o 6, pp. 1031–1044.