Distributed Adaptive Convex Optimization on Directed Graphs via Continuous-Time Algorithms
Distributed Adaptive Convex Optimization on Directed Graphs via Continuous-Time Algorithms
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DOI：
10.1109/tac.2017.2750103
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发表时间：
2018-05
影响因子：
6.8
通讯作者：
Zhenhong Li;Z. Ding;Junyong Sun;Zhongkui Li
中科院分区：
文献类型：
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作者：
Zhenhong Li;Z. Ding;Junyong Sun;Zhongkui Li
本文研究了具有非凸局部目标函数和网络连通度未知的有向图上的分布式优化问题。提出了一种新的自适应算法，以最小化一个可微的全局目标函数。通过引入动态耦合增益并利用系统状态的相对信息更新耦合增益，同时解决了局部目标函数的非凸性、未知网络连通性以及局部Lipschitz梯度引起的不确定动态问题。当全局目标函数是强凸的且局部目标函数的梯度仅为局部Lipschitz时，证明了算法的全局渐近收敛性。当通信图是强连通且权值平衡时，算法不依赖于任何全局信息。然后，利用Laplacian矩阵的左特征向量与零特征值相关联，将算法自然地推广到不平衡有向图。几个数值模拟来验证结果。
This note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity. A new adaptive algorithm is proposed to minimize a differentiable global objective function. By introducing dynamic coupling gains and updating the coupling gains using relative information of system states, the nonconvexity of local objective functions, unknown network connectivity, and the uncertain dynamics caused by locally Lipschitz gradients are tackled concurrently. Consequently, the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally Lipschitz. When the communication graph is strongly connected and weight-balanced, the algorithm is independent of any global information. Then, the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the Laplacian matrix associated with the zero eigenvalue. Several numerical simulations are presented to verify the results.