Accelerated Distributed Aggregative Optimization

• 成果类型: Article
• 署名作者: Liu, Jiaxu; Chen, Song; Cai, Shengze; Xu, Chao; Chu, Jian
• 署名单位: Zhejiang University; Zhejiang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3546096
• 发表日期: 2025
• 页码: 5792-5807
• 关键词: Optimization; CONVERGENCE; vectors; linear programming; cost function; Convex functions; chaos; training; Robustness; Industrial control; Aggregative optimization; distributed optimization; gradient tracking; heavy ball; jury criterion; Nesterov's accelerated method

摘要

This article delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on an aggregated function of state variables from all agents. To expedite the optimization process, we amalgamate the heavy ball and Nesterov's accelerated method with distributed aggregative gradient tracking, resulting in the proposal of two innovative algorithms, aimed at resolving the distributed aggregative optimization problem. Our analysis demonstrates that the proposed algorithms can converge to an optimal solution at a global linear convergence rate when the objective function is strongly convex with the Lipschitz-continuous gradient, and when the parameters (e.g., step size and momentum coefficients) are chosen within specific ranges. In addition, we present several numerical experiments to verify the effectiveness, robustness, and superiority of our proposed algorithms.