  In this paper we consider distributed optimization problems in which the cost
function is separable (i.e., a sum of possibly non-smooth functions all sharing
a common variable) and can be split into a strongly convex term and a convex
one. The second term is typically used to encode constraints or to regularize
the solution. We propose an asynchronous, distributed optimization algorithm
over an undirected topology, based on a proximal gradient update on the dual
problem. We show that by means of a proper choice of primal variables, the dual
problem is separable and the dual variables can be stacked into separate
blocks. This allows us to show that a distributed gossip update can be obtained
by means of a randomized block-coordinate proximal gradient on the dual
function.
