Explicit Convergence Rate of a Distributed Alternating Direction Method of Multipliers

Understand

Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents.

• The popular Alternating Direction Method of Multipliers has the potential to handle distributed optimization problems of this kind.
• We provide a general reformulation of the problem and obtain a class of distributed algorithms which encompass various network architectures.
• The rate of convergence of our method is considered.