Linearly Convergent Decentralized Consensus Optimization with the Alternating Direction Method of Multipliers
In 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.
Citable link to this pagehttps://hdl.handle.net/1911/102219
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- CAAM Technical Reports