参考文献：

[1] G. Monge. Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique et de Physique pour la même année, pages 666–704, 1781.

[2] L. Kantorovich. On the translocation of masses. C.R. (Doklady) Acad. Sci. URSS (N.S.), 37:199–201, 1942.

[3] Brenier Y. Polar factorization and monotone rearrangement of vector-valued functions. Communications on Pure and Applied Mathematics. 1991; 44(4):375–417.

[4] Gangbo W, McCann RJ. The geometry of optimal transportation. Acta Mathematica. 1996; 177(2):

113–161.

[5] Angenent S, Haker S, Tannenbaum A. Minimizing flows for the Monge--Kantorovich problem[J]. SIAM journal on mathematical analysis, 2003, 35(1): 61-97.

[6] Chartrand R, Wohlberg B, Vixie K, et al. A gradient descent solution to the Monge-Kantorovich problem[J]. Applied Mathematical Sciences, 2009, 3(22): 1071-1080.

[7] Cuturi, Marco. "Sinkhorn distances: Lightspeed computation of optimal transport." Advances in neural information processing systems(NIPS). 2013.

[8] Genevay, A., Cuturi, M., Peyré, G., & Bach, F. (2016). Stochastic optimization for large-scale optimal transport. In Advances in Neural Information Processing Systems (NIPS)(pp. 3440-3448).

[9] Dvurechensky, P., Gasnikov, A. & Kroshnin, A.. (2018). Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn’s Algorithm. Proceedings of the 35th International Conference on Machine Learning(ICML), in PMLR.80:1367-1376

[10] Villani C. Topics in optimal transportation[M]. American Mathematical Soc., 2003.

[11] Villani C. Optimal transport: old and new[M]. Springer Science & Business Media, 2008.

[12] Santambrogio F. Optimal transport for applied mathematicians[M]. Birkäuser, NY, 2015: 99-102.

[13] Peyré, G., & Cuturi, M. (2017). Computational optimal transport[M] (No. 2017-86).

[14] Seguy, V., & Cuturi, M. (2015). Principal geodesic analysis for probability measures under the optimal transport metric. In Advances in Neural Information Processing Systems(NIPS) (pp. 3312-3320).

[15] Courty, N., Flamary, R., & Ducoffe, M. (2018). Learning Wasserstein Embeddings. International Conference on Learning Representations(ICLR).

[16] M. Agueh and G. Carlier. Barycenters in the Wasserstein space. SIAM J. on Mathematical Analysis, 43(2):904–924, 2011.

[17] Ho, N., Nguyen, X., Yurochkin, M., Bui, H.H., Huynh, V., & Phung, D.Q. (2017). Multilevel Clustering via Wasserstein Means. ICML.

[18] Srivastava, S., Cevher, V., Dinh, Q. & Dunson, D.. (2015). WASP: Scalable Bayes via barycenters of subset posteriors. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics(AISTATS), in PMLR 38:912-920.

[19] Bonneel, N., Peyré, G., & Cuturi, M. (2016). Wasserstein barycentric coordinates: histogram regression using optimal transport. ACM Trans. Graph., 35(4), 71-1.

[20]Ye, J., Wu, P., Wang, J. Z., & Li, J. (2017). Fast discrete distribution clustering using Wasserstein barycenter with sparse support. IEEE Transactions on Signal Processing, 65(9), 2317-2332.

[21] Staib, M. Claici, S., Solomon, J. M., and Jegelka, S. Parallel streaming Wasserstein barycenters. In Advances in Neural Information Processing Systems(NIPS), pp. 2644–2655, 2017.

[22] Anderes, E. Borgwardt, S., and Miller, J. Discrete Wasserstein barycenters: Optimal transport for discrete data. Math Meth Oper Res, 84(2):389–409, October 2016. ISSN 1432-2994, 1432-5217. doi: 10.1007/s00186-016-0549-x.

[23] Claici, S., Chien, E., & Solomon, J. (2018). Stochastic Wasserstein Barycenters. ICML.

[24] G. Carlier, A. Oberman, and E. Oudet. Numerical methods for matching for teams and Wasserstein barycenters. Preprint hal-00987292, Preprint HAL-00987292, 2014.

[25] J-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyr´e. Iterative Bregman projectionsfor regularized transportation problems. SIAM Journal on Scientific Computing,37(2):A1111–A1138, 2015.

[26] M. Cuturi and A. Doucet. Fast computation of Wasserstein barycenters. In Proceedings of the 31st International Conference on Machine Learning (ICML-14), pages 685–693, 2014.