We study first order methods to compute the barycenter of a probability distribution $ P $
over the space of probability measures with finite second moment. We develop a framework …

We study the complexity of approximating the multimarginal optimal transport (MOT)
distance, a generalization of the classical optimal transport distance, considered here …

We study multi-marginal optimal transport problems from a probabilistic graphical model
perspective. We point out an elegant connection between the two when the underlying cost …

We consider stochastic convex optimization problems with affine constraints and develop
several methods using either primal or dual approach to solve it. In the primal case, we use …

We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …

Computing Wasserstein barycenters (aka optimal transport barycenters) is a fundamental
problem in geometry which has recently attracted considerable attention due to many …

Gaussian distributions are plentiful in applications dealing in uncertainty quantification and
diffusivity. They furthermore stand as important special cases for frameworks providing …

The optimal transport problem has recently developed into a powerful framework for various
applications in estimation and control. Many of the recent advances in the theory and …

We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in
computing the Wasserstein barycenter of $ m $ discrete probability measures supported on …

We study the computation of doubly regularized Wasserstein barycenters, a recently
introduced family of entropic barycenters governed by inner and outer regularization …