Linearly convergent decentralized consensus optimization with the alternating direction method of multipliers

ICASSP 2013, Vancouver, Canada

• Technical report

Overview

In a decentralized consensus optimization problem, a net- work of agents minimizes the summation of their local objec- tive 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 ac- celerate its convergence for decentralized consensus optimization problems.

Citation

W. Shi, Q. Ling, K. Yuan, G. Wu, and W. Yin, Linearly convergent decentralized consensus optimization with the alternating direction method of multipliers, in proceedings of International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, 2013