摘要
随着工业智能系统的快速发展以及能源互联网的广泛应用,工业软件在支持多节点协同计算和解决复杂优化问题中发挥了关键作用.然而,能源互联网的分布式、多节点自治特点以及复杂网络结构和实时动态调控需求,对工业软件的实时性、收敛速率和适用范围提出了更高要求.这些要求迫切需要设计高效的分布式优化算法作为工业软件的核心支撑.因此,本文研究了时变通信拓扑下的分布式非凸复合优化问题,其中全局目标函数由光滑的非凸部分和非光滑的凸部分组成.所提出的算法利用逐次凸逼近(successive convex approximation, SCA)技术与梯度跟踪机制,并引入类Nesterov动量项以调整每次迭代的更新方向,从而进一步提升算法的收敛速率.理论证明了当动量参数低于设定的上界时,所提算法在固定步长条件下能够渐近收敛至所研究问题的平衡点集.数值仿真实验进一步验证了算法的有效性.
With the rapid development of intelligent industrial systems and the widespread application of the energy internet,industrial software has played a critical role in supporting multi-node collaborative computation and solving complex optimization problems.However,the distributed and multi-node autonomous characteristics of the energy internet,along with its complex network structures and real-time dynamic regulation requirements,impose higher demands on the real-time performance,convergence rate,and applicability of industrial software.These requirements urgently necessitate the design of efficient distributed optimization algorithms as the core support for industrial software.Therefore,this paper investigates distributed non-convex composite optimization problems under time-varying communication topologies,where the global objective function comprises a smooth non-convex part and a non-smooth convex part.The proposed algorithm leverages the successive convex approximation(SCA)technique and gradient tracking mechanism,while incorporating a Nesterov-like momentum term to adjust the update direction in each iteration,thereby further enhancing the convergence rate of the algorithm.Theoretical analysis proves that,under a fixed step size and when the momentum parameter is below a specified upper bound,the proposed algorithm asymptotically converges to the equilibrium point set of the studied problem.Numerical simulations further validate the effectiveness of the algorithm.
作者
李天成
张坤朋
徐磊
高超
李凡
杨涛
Tiancheng LI;Kunpeng ZHANG;Lei XU;Chao GAO;Fan LI;Tao YANG(State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819,China)
出处
《中国科学:信息科学》
北大核心
2025年第7期1687-1700,共14页
Scientia Sinica(Informationis)
基金
国家自然科学基金重点项目(批准号:62133003)
国家重点研发计划课题(批准号:2022YFB3305904)资助。
关键词
工业软件
分布式非凸优化
复合优化
类Nesterov加速方法
industrial software
distributed non-convex optimization
composite optimization
Nesterov-like acceleration method
