Alternating Direction Method of Multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting agents locally estimate the optimal solution of an optimization problem and exchange messages with their neighbors over a connected network. The distributed algorithms are typically exposed to different types of errors in practice, e.g., due to quantization or communication noise or loss. We here focus on analyzing the convergence of distributed ADMM for consensus optimization in presence of additive random node error, in which case, the nodes communicate a noisy version of their latest estimate of the solution to their neighbors in each iteration. We present analytical upper and lower bounds on the mean squared steady state error of the algorithm in case that the local objective functions are strongly convex and have Lipschitz continuous gradients. In addition we show that, when the local objective functions are convex and the additive node error is bounded, the estimation error of the noisy ADMM for consensus optimization is also bounded. Numerical results are provided which demonstrate the effectiveness of the presented analyses and shed light on the role of the system and network parameters on performance.
Waveform Design for ISAC System: A Consensus ADMM Approach
VNU University of Engineering and Technology（越南国立大学工程技术大学）；National Foundation for Science and Technology Development（国家科学技术发展基金会）；Posts and Telecommunications Institute of Technology（邮电技术研究所）
