  In this paper we consider a network with $P$ nodes, where each node has
exclusive access to a local cost function. Our contribution is a
communication-efficient distributed algorithm that finds a vector $x^\star$
minimizing the sum of all the functions. We make the additional assumption that
the functions have intersecting local domains, i.e., each function depends only
on some components of the variable. Consequently, each node is interested in
knowing only some components of $x^\star$, not the entire vector. This allows
for improvement in communication-efficiency. We apply our algorithm to model
predictive control (MPC) and to network flow problems and show, through
experiments on large networks, that our proposed algorithm requires less
communications to converge than prior algorithms.
