  We consider the problem of minimizing the sum of non-smooth convex functions
in non-Euclidean spaces, e.g., probability simplex, via only local computation
and communication on an undirected graph. We propose two algorithms motivated
by mass-spring-damper dynamics. The first algorithm uses an explicit update
that computes subgradients and Bregman projections only, and matches the
convergence behavior of centralized mirror descent. The second algorithm uses
an implicit update that solves a penalized subproblem at each iteration, and
achieves the iteration complexity of \(\mathcal{O}(1/K)\). The results are also
demonstrated via numerical examples.
