Title: Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Error,
Abstract: ADMM is a popular algorithm for solving convex optimization problems.
Applying this algorithm to distributed consensus optimization problem results
in a fully distributed iterative solution which relies on processing at the
nodes and communication between neighbors. Local computations usually suffer
from different types of errors, due to e.g., observation or quantization noise,
which can degrade the performance of the algorithm. In this work, we focus on
analyzing the convergence behavior of distributed ADMM for consensus
optimization in presence of additive node error. We specifically show that (a
noisy) ADMM converges linearly under certain conditions and also examine the
associated convergence point. Numerical results are provided which demonstrate
the effectiveness of the presented analysis.