Shi, W.Ling, Q.Yuan, K.Wu, G.Yin, W.2018-06-192018-06-192013-04Shi, W., Ling, Q., Yuan, K., et al.. "Linearly Convergent Decentralized Consensus Optimization with the Alternating Direction Method of Multipliers." (2013) <a href="https://hdl.handle.net/1911/102219">https://hdl.handle.net/1911/102219</a>.https://hdl.handle.net/1911/102219In a decentralized consensus optimization problem, a network of agents minimizes the summation of their local objective functions on a common set of decision variables, allowing only information exchange among neighbors. The alternating direction method of multipliers (ADMM) has been shown to be a powerful tool for solving the problem with empirically fast convergence. This paper establishes the linear convergence rate of the ADMM in decentralized consensus optimization. The theoretical convergence rate is a function of the network topology, properties of the local objective functions, and the algorithm parameter. This result not only gives a performance guarantee for the ADMM but also provides a guideline to accelerate its convergence for decentralized consensus optimization problems.5 ppengTechnical reportTR13-07