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This chapter describes techniques for the numerical resolution of optimal transport problems.
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Fernando De Goes, Katherine Breeden, Victor Ostromoukhov, and Mathieu Desbrun, Blue noise through optimal transport , ACM Transactions on Graphics (TOG) 31
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Victor Chernozhukov, Alfred Galichon, Marc Hallin, Marc Henry, et al., Monge–kantorovich depth, quantiles, ranks and signs , The Annals of Statistics 45
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2018
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Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard, An interpolating distance between optimal transport and fisher–rao metrics , Foundations of Computational Mathematics 18
2018
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Marco Cuturi and Gabriel Peyré, Semidual regularized optimal transport , SIAM Review 60
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2018
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Bruno Galerne, Arthur Leclaire, and Julien Rabin, A texture synthesis model based on semi-discrete optimal transport in patch space , SIAM Journal on Imaging Sciences 11
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Alfred Galichon, Optimal transport methods in economics , Princeton University Press, 2018
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Quentin Mérigot, Jocelyn Meyron, and Boris Thibert, An algorithm for optimal transport between a simplex soup and a point cloud , SIAM Journal on Imaging Sciences 11
2018
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2019
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Jean-David Benamou and Vincent Duval, Minimal convex extensions and finite difference discretisation of the quadratic monge–kantorovich problem , European Journal of Applied Mathematics 30
2019
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2019
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by same author, Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure , Numerische Mathematik 141
2019
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Jean Feydy, Pierre Roussillon, Alain Trouvé, and Pietro Gori, Fast and scalable optimal transport for brain tractograms , International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer, 2019, pp. 636–644
2019
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2019
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Jun Kitagawa, Quentin Mérigot, and Boris Thibert, Convergence of a newton algorithm for semi-discrete optimal transport , Journal of the European Mathematical Society (2019), OnlineFirst
2019
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2019
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2019
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Jocelyn Meyron, Quentin Mérigot, and Boris Thibert, Light in power: a general and parameter-free algorithm for caustic design , ACM Transactions on Graphics (TOG) 37
2019
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2019
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Gabriel Peyré and Marco Cuturi, Computational optimal transport , Foundations and Trends® in Machine Learning 11
2019
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by same author, Stabilized sparse scaling algorithms for entropy regularized transport problems , SIAM Journal on Scientific Computing 41
2019
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François-Xavier Vialard, An elementary introduction to entropic regularization and proximal methods for numerical optimal transport , Lecture, May 2019
2019
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