  Distributed decision problems features a group of agents that can only
communicate over a peer-to-peer network, without a central memory. In
applications such as network control and data ranking, each agent is only
affected by a small portion of the decision vector: this sparsity is typically
ignored in distributed algorithms, while it could be leveraged to improve
efficiency and scalability. To address this issue, our recent paper introduces
Estimation Network Design (END), a graph theoretical language for the analysis
and design of distributed iterations. END algorithms can be tuned to exploit
the sparsity of specific problem instances, reducing communication overhead and
minimizing redundancy, yet without requiring case-by-case convergence analysis.
In this paper, we showcase the flexility of END in the context of distributed
optimization. In particular, we study the sparsity-aware version of many
established methods, including ADMM, AugDGM and Push-Sum DGD. Simulations on an
estimation problem in sensor networks demonstrate that END algorithms can boost
convergence speed and greatly reduce the communication and memory cost.
