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This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport.
C. Léonard, From the schrödinger problem to the monge–kantorovich problem , Journal of Functional Analysis 262
1920
Earlier work this paper cites.
E. Schrödinger, Über die Umkehrung der Naturgesetze , Sitzungsberichte Preuss. Akad. Wiss. Berlin. Phys. Math. 144
1931
Earlier work this paper cites.
W. E. Deming and F. F. Stephan, On a least squares adjustment of a sampled frequency table when the expected marginal totals are known , Annals Mathematical Statistics 11
1940
Earlier work this paper cites.
L. Kantorovich, On the transfer of masses (in russian) , Doklady Akademii Nauk 37
1942
Earlier work this paper cites.
A.C. Thompson, On certain contraction mappings in a partially ordered vector space , Proceedings of the American Mathematical Society 14
1963
Earlier work this paper cites.
R. Sinkhorn, A relationship between arbitrary positive matrices and doubly stochastic matrices , Ann. Math. Statist. 35
1964
Earlier work this paper cites.
L. M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , USSR computational mathematics and mathematical physics 7
1967
Earlier work this paper cites.
R.T. Rockafellar, Duality and stability in extremum problems involving convex functions , Pacific Journal of Mathematics 21
1967
Earlier work this paper cites.
by same author, Integrals which are convex functionals , Pacific journal of mathematics 24
1968
Earlier work this paper cites.
by same author, Integral functionals, normal integrands and measurable selections , Nonlinear operators and the calculus of variations, Springer, 1976, pp. 157–207
1976
Earlier work this paper cites.
R. L. Dykstra, An algorithm for restricted least squares regression , J. Amer. Stat. 78
1983
Earlier work this paper cites.
D. Bertsekas and D. Castanon, The auction algorithm for the transportation problem , Annals of Operations Research 20
1989
Earlier work this paper cites.
J. Franklin and J. Lorenz, On the scaling of multidimensional matrices , Linear Algebra and its applications 114
1989
Earlier work this paper cites.
Jonathan M Borwein and Adrian S Lewis, Duality relationships for entropy-like minimization problems , SIAM Journal on Control and Optimization 29
1991
Earlier work this paper cites.
Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions , Comm. Pure Appl. Math. 44
1991
Earlier work this paper cites.
L. G. Hanin, Kantorovich-Rubinstein norm and its application in the theory of Lipschitz spaces , Proceedings of the American Mathematical Society 115
1992
Earlier work this paper cites.
J. Eckstein, Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming , Mathematics of Operations Research 18
1993
Earlier work this paper cites.
J.J. Kosowsky and A.L. Yuille, The invisible hand algorithm: Solving the assignment problem with statistical physics , Neural Networks 7
1994
Earlier work this paper cites.
F. Aurenhammer, F. Hoffmann, and B. Aronov, Minkowski-type theorems and least-squares clustering , Algorithmica 20
1998
Earlier work this paper cites.
Y. Censor and S. Reich, The Dykstra algorithm with Bregman projections , Communications in Applied Analysis 2
1998
Earlier work this paper cites.
R. Jordan, D. Kinderlehrer, and O. Otto, The variational formulation of the Fokker-Planck equation , SIAM journal on mathematical analysis 29
1998
Earlier work this paper cites.
H. H. Bauschke and A. S. Lewis, Dykstra’s algorithm with Bregman projections: a convergence proof , Optimization 48
2000
Earlier work this paper cites.
J-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , Numerische Mathematik 84
2000
Earlier work this paper cites.
Y. Rubner, C. Tomasi, and L.J. Guibas, The earth mover’s distance as a metric for image retrieval , International Journal of Computer Vision 40
2000
Earlier work this paper cites.
F. Otto, The geometry of dissipative evolution equations: the porous medium equation , Communications in partial differential equations 26
2001
Earlier work this paper cites.
C. Villani, Topics in optimal transportation , American Mathematical Soc., 2003
2003
Earlier work this paper cites.
J. Delon, Movie and video scale-time equalization application to flicker reduction , IEEE Transactions on Image Processing 15
2006
Cited alongside, same era.
F. Pitié, A.C. Kokaram, and R. Dahyot, Automated colour grading using colour distribution transfer , Computer Vision and Image Understanding 107
2007
Cited alongside, same era.
L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures , Springer Science & Business Media, 2008
2008
Cited alongside, same era.
R. Burkard, M. Dell’Amico, and S. Martello, Assignment problems , Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2009
2009
Cited alongside, same era.
A. Galichon and B. Salanié, Matching with trade-offs: Revealed preferences over competing characteristics , Tech. report, Preprint SSRN-1487307, 2009
2009
J. Solomon, R.M. Rustamov, L. Guibas, and A. Butscher, Wasserstein propagation for semi-supervised learning , Proc. ICML 2014, 2014
2014
Later among the works it cites.
2014
Later among the works it cites.
M. Agueh, B. Khouider, and L-P. Saumier, Optimal transport for particle image velocimetry , Communications in Mathematical Sciences 13
2015
Later among the works it cites.
A. Beck, On the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition schemes , SIAM Journal on Optimization 25
2015
Later among the works it cites.
J-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré, Iterative Bregman projections for regularized transportation problems , SIAM Journal on Scientific Computing 37
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Cited alongside, same era.
R.T. Rockafellar and R. J-B. Wets, Variational analysis , vol. 317, Springer Science & Business Media, 2009
2009
Cited alongside, same era.
C. Villani, Optimal transport: Old and new , Grundlehren der mathematischen Wissenschaften, vol. 338, Springer, 2009
2009
Cited alongside, same era.
M. Burger, J. A. Carrillo, and M-T. Wolfram, A mixed finite element method for nonlinear diffusion equations , Kinetic and Related Models 3
2010
Cited alongside, same era.
L. A. Caffarelli and R. J. McCann, Free boundaries in optimal transport and monge-ampere obstacle problems , Annals of mathematics (2010), 673–730
2010
Cited alongside, same era.
A. Figalli, The optimal partial transport problem , Archive for rational mechanics and analysis 195
2010
Cited alongside, same era.
B. Maury, A. Roudneff-Chupin, and F. Santambrogio, A macroscopic crowd motion model of gradient flow type , Mathematical Models and Methods in Applied Sciences 20
2010
Cited alongside, same era.
M. Agueh and G. Carlier, Barycenters in the Wasserstein space , SIAM Journal on Mathematical Analysis 43
2011
Cited alongside, same era.
2015
Later among the works it cites.
Jean-David Benamou, Guillaume Carlier, and Maxime Laborde, An augmented lagrangian approach to wasserstein gradient flows and applications , (2015)
2015
Later among the works it cites.
G. Carlier, V. Duval, G. Peyré, and B. Schmitzer, Convergence of entropic schemes for optimal transport and gradient flows , Preprint 01235146, HAL, 2015
2015
Later among the works it cites.
J. A. Carrillo, A. Chertock, and Y. Huang, A finite-volume method for nonlinear nonlocal equations with a gradient flow structure , Communications in Computational Physics 17
2015
Later among the works it cites.
L. Chizat, G. Peyré, B. Schmitzer, and F-X. Vialard, Unbalanced optimal transport: Geometry and kantorovich formulation , Preprint 1508.05216, Arxiv, 2015
2015
Later among the works it cites.
L. Chizat, B. Schmitzer, G. Peyré, and F-X. Vialard, An interpolating distance between optimal transport and Fischer-Rao , Preprint 1506.06430, Arxiv, 2015
2015
Later among the works it cites.
C. Frogner, C. Zhang, H. Mobahi, M. Araya-Polo, and T. Poggio, Learning with a Wasserstein loss , Preprint 1506.05439, Arxiv, 2015
2015
Later among the works it cites.
T. O. Gallouet and L. Monsaingeon, A JKO splitting scheme for Kantorovitch-Fisher-Rao gradient flows , Preprint arXiv (2015)
2015
Later among the works it cites.
S. Kondratyev, L. Monsaingeon, and D. Vorotnikov, A new optimal transport distance on the space of finite Radon measures , Tech. report, Pre-print, 2015
2015
Later among the works it cites.
2015
Later among the works it cites.
B. Levy, A numerical algorithm for L 2 L^{2} semi-discrete optimal transport in 3d , M2AN, to appear (2015)
2015
Later among the works it cites.
M. Liero, A. Mielke, and G. Savaré, Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures , ArXiv e-prints (2015)
2015
Later among the works it cites.
by same author, Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves , ArXiv e-prints (2015)
2015
Later among the works it cites.
2015
Later among the works it cites.
Q. V. Nguyen, Forward-backward splitting with Bregman distances , arXiv:1505.05198 (2015)
2015
Later among the works it cites.
G. Peyré, Entropic approximation of Wasserstein gradient flows , SIAM Journal on Imaging Sciences 8
2015
Later among the works it cites.
J. Rabin and N. Papadakis, Convex color image segmentation with optimal transport distances , Proc. SSVM’15, 2015
2015
Later among the works it cites.
F. Santambrogio, Optimal transport for applied mathematicians , Birkhauser, 2015
2015
Later among the works it cites.
J. Solomon, F. de Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas, Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains , ACM Transactions on Graphics (Proc. SIGGRAPH 2015) 34
2015
Later among the works it cites.
Jonathan Zinsl and Daniel Matthes, Transport distances and geodesic convexity for systems of degenerate diffusion equations , Calculus of Variations and Partial Differential Equations 54
2015
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B. Schmitzer, A sparse multiscale algorithm for dense optimal transport , J Math Imaging Vis 56
2016
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