一种扩展的分布式非精确多更新单组合算法  

An Extended Distributed Inexact Method with Multi-Update and Single-Combination Strategy

作　　者：郝晓惠 肖艳阳 

机构地区：[1]河北工业大学理学院,天津

出　　处：《应用数学进展》2025年第1期410-422,共13页Advances in Applied Mathematics

摘　　要：在这项工作中,我们提出了一种基于扩展梯度的分布式非精确单更新多组合算法(简称ExtendMUSIC)。该方法利用前两次迭代的梯度和来构造搜索方向,再利用多次局部更新然后定期组合的策略来求解光滑强凸的分布式优化问题。此外,我们证明了所提出的算法能够实现线性收敛。数值实验结果表明,与不使用扩展梯度的分布式多更新单组合算法相比,扩展的分布式多更新单组合算法可以实现加速收敛。In this work, we propose a distributed inexact multi-update and single-combination algorithm based on extended gradients (ExtendMUSIC). This method utilizes the gradient sum of the first two iterations to construct the search direction, and then uses the strategy of multiple local updates and periodic combinations to solve smooth and strongly convex distributed optimization problems. In addition, we prove that the proposed algorithm can achieve linear convergence. The numerical experimental results show that compared with the distributed multi-update and single-combination algorithm without using extended gradients, the extended distributed multi-update and single-combination algorithm can achieve accelerated convergence.

关 键 词：分布式优化 多更新单组合 扩展梯度下降法 线性收敛 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]