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Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems
Open accessAbstract
The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of ℓ2-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.
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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
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Bi, S., & Zhang, Y. J. (2018) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2018.2821664 · Cited by 870
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Garone, E., Di Cairano, S., & Kolmanovsky, I. (2017) · Automatica · doi:10.1016/j.automatica.2016.08.013 · Cited by 466
Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers
Gambella, C., & Simonetto, A. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.3033139 · Cited by 60
Li, B., & Xu, Q. (2024) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2023.3279303 · Cited by 31
Adajania, V. K., Zhou, S., Singh, A. K., & Schoellig, A. P. (2023) · 2023 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra48891.2023.10161063 · Cited by 23
Metadata
- Authors
- Ghadimi, E., Teixeira, A., Shames, I., & Johansson, M.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2015-03
- Volume
- 60
- Issue
- 3
- Pages
- 644-658
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2037603831
- Cited by
- 437
- References
- 2
- FWCI
- 31.34
- Type
- journal article
- Language
- en
- Open access
- green
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- Ghadimi, E., Teixeira, A., Shames, I., & Johansson, M. (2015). Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2014.2354892
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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