  We consider distributed convex-concave saddle point problems over arbitrary
connected undirected networks and propose a decentralized distributed algorithm
for their solution. The local functions distributed across the nodes are
assumed to have global and local groups of variables. For the proposed
algorithm we prove non-asymptotic convergence rate estimates with explicit
dependence on the network characteristics. To supplement the convergence rate
analysis, we propose lower bounds for strongly-convex-strongly-concave and
convex-concave saddle-point problems over arbitrary connected undirected
networks. We illustrate the considered problem setting by a particular
application to distributed calculation of non-regularized Wasserstein
barycenters.
