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Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design
IEEE Transactions on Cybernetics ( IF 11.8 ) Pub Date : 2023-05-09 , DOI: 10.1109/tcyb.2023.3270185
Meng Luan , Guanghui Wen , Hongzhe Liu , Tingwen Huang , Guanrong Chen , Wenwu Yu

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.

中文翻译:

具有闭凸集约束的分布式离散时间凸优化:线性收敛算法设计

收敛速度和对具有交互拓扑的有向图的适用性是分布式优化算法实际应用的两个重要特征。在本文中,开发了一种新型快速分布式离散时间算法,用于解决有向交互网络上具有闭凸集约束的凸优化问题。在梯度跟踪框架下,分别在平衡图和不平衡图上设计了两种分布式算法,其中涉及动量项和两个时间尺度。此外,结果表明,只要适当选择动量系数和步长,所设计的分布式算法即可实现线性加速收敛速度。最后,数值模拟验证了所设计算法的有效性和全局加速效果。
更新日期:2023-05-09
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