Section: New Results

Multi-marginal problems

• [Carlier, Oberman (Univ. Mc Gill), Oudet (Univ. of Grenoble) - New numerical methods for the Wasserstein barycenter and related multi-marginals problems were investigated [49] . A first method uses linear programming, in an implementation that was more efficient than expected. A second method takes advantage of the quadratic structure and leads to an efficient algorithm that can be used in texture synthesis problems arising in image processing.

  Figure 4. Texture mixing with Wasserstein barycenters, from top to bottom three densities and their barycenter.

• Benamou, Carlier, Nenna Extension of the CFD formulation and the ALG2 algorithm to the multi marginal problem with quadratic cost (Barycenter).