38 citations · 134 across the 17 of their papers we have counts for
5 papers · 1 filter
Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, Quentin Merigot
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or l…
Optimal transport: discretization and algorithms
Quentin Merigot, Boris Thibert
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong f…
Minimal geodesics along volume preserving maps, through semi-discrete optimal transport
Quentin Mérigot, Jean-Marie Mirebeau
We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L2 metric, which as observed by Arnold solve Euler's e…
Discretization of functionals involving the Monge-Ampère operator
Jean-David Benamou, Guillaume Carlier, Quentin Mérigot +1
Gradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The n…
Handling convexity-like constraints in variational problems
Quentin Mérigot, Edouard Oudet
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the spa…