Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs
Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs
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DOI：
10.1109/tac.2013.2278132
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发表时间：
2014-03-01
影响因子：
6.8
通讯作者：
Cortes, Jorge
中科院分区：
文献类型：
--
作者：
Gharesifard, Bahman;Cortes, Jorge
该技术说明研究了在有向图上的凸函数总和的连续分布式优化。与共识文献中所知的相反，相同的动态适用于无向和有向情景，我们表明，基于共识的动力学解决了无向图的连续时间分布式优化问题，当转发为有向的时，环境。这项研究为设计替代分布式动力学设计的基础设定了基础，我们证明，该动力学可以在任何紧密连接的重量平衡的挖掘物上收敛到具有全球Lipschitz梯度的凸线可区分函数总和的一组最小化器。我们的技术方法将不变性和可核性的概念与图矩阵的积极确定性特性结合在一起，以建立结果。
This technical note studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge, on any strongly connected weight-balanced digraph, to the set of minimizers of a sum of convex differentiable functions with globally Lipschitz gradients. Our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results.