H. Attouch, J. Bolte, and B. Svaiter, Convergence of descent methods for semialgebraic and tame problems Agueh and G. Carlier. Barycenters in the Wasserstein space, Mathematical Programming, pp.91-129904, 2011.

[. Ambrosio, N. Gigli, and G. Savaré, Gradient flows with metric and differentiable structures, and applications to the Wasserstein space, Atti Accad. Naz. Lincei Cl

[. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures, 2006.

[. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré, Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.1111-1138, 2015.
DOI : 10.1137/141000439

URL : https://hal.archives-ouvertes.fr/hal-01096124

J. Bigot, R. Gouet, T. Klein, and A. Lopez, Geodesic PCA in the Wasserstein space by Convex PCA. Annales de l'Institut Henri Poincaré B: Probability and Statistics, 2015.

]. Y. Bre91 and . Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on pure and applied mathematics, vol.44, issue.4, pp.375-417, 1991.

T. [. Chambolle and . Pock, On the ergodic convergence rates of a first-order primaldual algorithm, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01151629

T. [. Chambolle and . Pock, On the ergodic convergence rates of a first-order primal , ¨ A` ?dual algorithm, Mathematical Programming, pp.1-35, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01151629

L. Craig, E. Ronald, and F. Gariepy, Measure theory and fine properties of functions, 2015.

P. T. Fletcher, C. Lu, S. M. Pizer, and S. Joshi, Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape, IEEE Transactions on Medical Imaging, vol.23, issue.8, pp.995-1005, 2004.
DOI : 10.1109/TMI.2004.831793

G. Steven, . Krantz, R. Harold, and . Parks, Geometric integration theory, 2008.

]. Y. Lec98 and . Lecun, The mnist database of handwritten digits, 1998.

T. [. Lorenz and . Pock, An Inertial Forward-Backward Algorithm for Monotone Inclusions, Journal of Mathematical Imaging and Vision, vol.23, issue.3, pp.311-325, 2015.
DOI : 10.1137/110844805

URL : http://arxiv.org/abs/1403.3522

P. Ochs, Y. Chen, T. Brox, T. [. Pock, H. Petersen et al., iPiano: Inertial Proximal Algorithm for Nonconvex Optimization, Advances in Neural Information Processing Systems 28, pp.1388-1419183, 2014.
DOI : 10.1137/130942954

URL : http://arxiv.org/abs/1404.4805

F. [. Sommer, S. Lauze, M. Hauberg, and . Nielsen, Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations, Kostas Daniilidis , Petros Maragos, and Nikos Paragios Computer Vision ECCV 2010, pp.43-56, 2010.
DOI : 10.1007/978-3-642-15567-3_4

A. [. Verde, A. Irpino, and . Balzanella, Dimension Reduction Techniques for Distributional Symbolic Data, IEEE Transactions on Cybernetics, vol.46, issue.2, pp.344-355, 2003.
DOI : 10.1109/TCYB.2015.2389653

]. W. Wsb-+-13, D. Wang, S. Slepcev, J. A. Basu, G. K. Ozolek et al., A linear optimal transportation framework for quantifying and visualizing variations in sets of images, International Journal of Computer Vision, vol.101, issue.2, pp.254-269, 2013.