论文标题
Wang-Elia算法的稳定性，线性收敛和鲁棒性，用于分布式共识优化
Stability, Linear Convergence, and Robustness of the Wang-Elia Algorithm for Distributed Consensus Optimization
论文作者
论文摘要
我们对J. Wang和N. Elia在2010年提出的分布式共识优化进行了重新审视算法。通过基于lyapunov的分析，我们证明算法相对于由最佳平衡组成的封闭不变套件的输入到状态稳定性，以及影响算法动力学的扰动。在没有扰动的情况下，该结果意味着最佳稳态的局部估计值和Lyapunov稳定性的线性收敛。此外，我们与众所周知的梯度跟踪以及分布式积分控制介绍了基本联系。总体而言，我们的结果表明，控制理论方法可以对（分布式）优化产生重大影响，尤其是在考虑鲁棒性时。
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 well-known 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.
