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We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs.
1905
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Quentin Mérigot, A multiscale approach to optimal transport , Computer Graphics Forum, vol. 30, Wiley Online Library, 2011, pp. 1583–1592
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Jean-David Benamou, Brittany D. Froese, and Adam M. Oberman, Numerical solution of the optimal transportation problem using the Monge–Ampère equation , J. Comput. Phys. 260
2013
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Marco Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport , Proceedings of the 26th International Conference on Neural Information Processing Systems - Volume 2 (USA), NIPS’13, Curran Associates Inc., 2013, pp. 2292–2300, http://dl.acm.org/citation.cfm?id=2999792.2999868
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Bruno Lévy, A numerical algorithm for L 2 L_{2} semi-discrete optimal transport in 3D , ESAIM Math. Model. Numer. Anal. 49
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Steven Haker, Lei Zhu, Allen Tannenbaum, and Sigurd Angenent, Optimal mass transport for registration and warping , International Journal of computer vision 60
2004
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Yurii Nesterov, Introductory lectures on convex optimization , Applied Optimization, vol. 87, Kluwer Academic Publishers, Boston, MA, 2004, A basic course, doi:10.1007/978-1-4419-8853-9
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Minyi Huang, Roland P. Malhamé, and Peter E. Caines, Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle , Commun. Inf. Syst. 6
2006
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Jean-Michel Lasry and Pierre-Louis Lions, Mean field games , Jpn. J. Math. 2
2007
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Rick Chartrand, Brendt Wohlberg, Kevin R. Vixie, and Erik M. Bollt, A gradient descent solution to the Monge–Kantorovich problem , Appl. Math. Sci. (Ruse) 3
2009
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C. R. Prins, R. Beltman, J. H. M. ten Thije Boonkkamp, W. L. Ijzerman, and T. W. Tukker, A least-squares method for optimal transport using the Monge–Ampère equation , SIAM J. Sci. Comput. 37
2015
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Filippo Santambrogio, Optimal transport for applied mathematicians , Progress in Nonlinear Differential Equations and their Applications, vol. 87, Birkhäuser/Springer, Cham, 2015, Calculus of variations, PDEs, and modeling, doi:10.1007/978-3-319-20828-2
2015
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Quentin Mérigot and Jean-Marie Mirebeau, Minimal geodesics along volume-preserving maps, through semidiscrete optimal transport , SIAM J. Numer. Anal. 54
2016
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Martin Arjovsky, Soumith Chintala, and Léon Bottou, Wasserstein generative adversarial networks , Proceedings of the 34th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 70, PMLR, 06–11 Aug 2017, pp. 214–223, http://proceedings.mlr.press/v70/arjovsky17a.html
2017
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Michael Lindsey and Yanir A. Rubinstein, Optimal transport via a Monge–Ampère optimization problem , SIAM J. Math. Anal. 49
2017
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Thomas O. Gallouët and Quentin Mérigot, A Lagrangian scheme à la Brenier for the incompressible Euler equations , Found. Comput. Math. 18
2018
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