Generalized consensus computation in networked systems with erasure links

We study consensus problems in networked systems with unreliable links. Our contributions are two-fold. First, we derive a family of decentralized consensus algorithms for minimizing a sum of convex functions, Σ_i=1^Nf_i(x), where each function f_i only depends on information at one node in the network. Computing the consensus average is a special case in this setting. Then, we construct a modified algorithm which is resilient in situations where the channels between nodes act as binary erasure channels. The flexibility and efficacy of our approach is demonstrated through an application of robust estimation.