  We consider a multimarginal optimal transport, which includes as a particular
case the Wasserstein barycenter problem. In this problem one has to find an
optimal coupling between $m$ probability measures, which amounts to finding a
tensor of the order $m$. We propose an accelerated method based on accelerated
alternating minimization and estimate its complexity to find the approximate
solution to the problem. We use entropic regularization with sufficiently small
regularization parameter and apply accelerated alternating minimization to the
dual problem. A novel primal-dual analysis is used to reconstruct the
approximately optimal coupling tensor. Our algorithm exhibits a better
computational complexity than the state-of-the-art methods for some regimes of
the problem parameters.
