Accelerated Distributed Aggregative Optimization
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908290100756480 |
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| author | Liu, Jiaxu Chen, Song Cai, Shengze Xu, Chao Chu, Jian |
| author_facet | Liu, Jiaxu Chen, Song Cai, Shengze Xu, Chao Chu, Jian |
| contents | This paper 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 Nesterovs 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. Additionally, we present several numerical experiments to verify the effectiveness, robustness and superiority of our proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerated Distributed Aggregative Optimization Liu, Jiaxu Chen, Song Cai, Shengze Xu, Chao Chu, Jian Optimization and Control This paper 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 Nesterovs 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. Additionally, we present several numerical experiments to verify the effectiveness, robustness and superiority of our proposed algorithms. |
| title | Accelerated Distributed Aggregative Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.23325 |