We revisit an algorithm for distributed consensus optimization proposed in 2010 by J. Wang and N. Elia. By means of a Lyapunov-based analysis, we prove input-to-state stability of the algorithm relative to a closed invariant set composed of optimal equilibria and with respect to perturbations affecting the algorithm's dynamics. In the absence of perturbations, this result implies linear convergence of the local estimates and Lyapunov stability of the optimal steady state. Moreover, we unveil fundamental connections with the wellknown Gradient Tracking and with distributed integral control. Overall, our results suggest that a control theoretic approach can have a considerable impact on (distributed) optimization, especially when robustness is considered.

Bin M., Notarnicola I., Parisini T. (2022). Stability, Linear Convergence, and Robustness of the Wang-Elia Algorithm for Distributed Consensus Optimization. Institute of Electrical and Electronics Engineers Inc. [10.1109/CDC51059.2022.9993284].

Stability, Linear Convergence, and Robustness of the Wang-Elia Algorithm for Distributed Consensus Optimization

Bin M.
Primo
;
Notarnicola I.;
2022

Abstract

We revisit an algorithm for distributed consensus optimization proposed in 2010 by J. Wang and N. Elia. By means of a Lyapunov-based analysis, we prove input-to-state stability of the algorithm relative to a closed invariant set composed of optimal equilibria and with respect to perturbations affecting the algorithm's dynamics. In the absence of perturbations, this result implies linear convergence of the local estimates and Lyapunov stability of the optimal steady state. Moreover, we unveil fundamental connections with the wellknown Gradient Tracking and with distributed integral control. Overall, our results suggest that a control theoretic approach can have a considerable impact on (distributed) optimization, especially when robustness is considered.
2022
Proceedings of the IEEE Conference on Decision and Control
1610
1615
Bin M., Notarnicola I., Parisini T. (2022). Stability, Linear Convergence, and Robustness of the Wang-Elia Algorithm for Distributed Consensus Optimization. Institute of Electrical and Electronics Engineers Inc. [10.1109/CDC51059.2022.9993284].
Bin M.; Notarnicola I.; Parisini T.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/916930
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