Distributed Optimization on Unbalanced Time-Varying Topologies: Theories and Experiments
Distributed Optimization on Unbalanced Time-Varying Topologies: Theories and Experiments
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DOI：
10.23919/chicc.2018.8484051
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Zhenhong Li;Tianqiao Zhao;Z. Ding
中科院分区：
文献类型：
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作者：
Zhenhong Li;Tianqiao Zhao;Z. Ding
本文考虑了在连续时间框架内固定和时变有向通信结构上的分布式优化问题。与已有的连续时间优化结果不同，该算法不需要局部凸性常数的下界，也不需要权平衡的通信结构.设计了一个增广拉格朗日函数，分析了非对称拉普拉斯矩阵上最优解的性质。在此基础上，提出了一种基于共识的算法来求解非平衡有向图上的分布式优化问题，使得算法渐近收敛于最优解。在此基础上，提出了一种求解非平衡时变通信拓扑上分布式优化问题的算法。设计了一种新的包含半正定项的李雅普诺夫函数来分析该算法的收敛性。通过研究正不变集和非对称Laplacian矩阵的某些性质，给出了收敛的充分条件。在分布式微机平台上进行了两个实验，从而验证了所提出的算法。
This paper considers distributed optimization problems on both fixed and time-varying directed communication structures within a continuous-time framework. Different from most existing results in literature on continuous-time optimization, the lower bound of local convexity constants are unknown, and the requirement of weight-balanced communication structures is removed. An augmented Lagrangian function is designed to analyze the properties of optimal solutions over an asymmetric Laplacian matrix. Based on this analysis, a consensus-based algorithm is proposed to solve the distributed optimization problem on unbalanced directed graphs such that the algorithm asymptotically converges to optimal solutions. Furthermore, an algorithm is proposed to solve the distributed optimization problem on unbalanced time-varying communication topologies. A novel Lyapunov function including a semi-positive definite term is designed to establish the convergence analysis of this algorithm. By exploring certain features of positive invariance sets and asymmetric Laplacian matrices, sufficient conditions for the convergence are established. Two experiments are carried out on a distributed microcomputer platform, thus validating the proposed algorithms.