Distributed Optimization with Local Domains: Applications in MPC and Network Flows

We consider a network where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector 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 star, not the entire vector. This allows improving communication-efficiency. We apply our algorithm to distributed model predictive control (D-MPC) and to network flow problems and show, through experiments on large networks, that the proposed algorithm requires less communications to converge than prior state-of-the-art algorithms.