A Unified Algorithm for Nonconvex Decentralized Nonlinear Optimization
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908956267380736 |
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| author | Wu, Hao Wang, Liping |
| author_facet | Wu, Hao Wang, Liping |
| contents | In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized nonconvex algorithmic framework that includes many existing state-of-the-art gradient tracking and quasi-Newton algorithms. A general framework for the convergence analysis of our unified algorithm is presented under both nonconvex and the Kurdyka-Łojasiewicz condition settings. In particular, some new quasi-Newton algorithms under this framework are proposed. Our numerical results show that these newly developed algorithms are very efficient compared with other state-of-the-art algorithms for solving decentralized nonconvex nonlinear optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Algorithm for Nonconvex Decentralized Nonlinear Optimization Wu, Hao Wang, Liping Optimization and Control In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized nonconvex algorithmic framework that includes many existing state-of-the-art gradient tracking and quasi-Newton algorithms. A general framework for the convergence analysis of our unified algorithm is presented under both nonconvex and the Kurdyka-Łojasiewicz condition settings. In particular, some new quasi-Newton algorithms under this framework are proposed. Our numerical results show that these newly developed algorithms are very efficient compared with other state-of-the-art algorithms for solving decentralized nonconvex nonlinear optimization. |
| title | A Unified Algorithm for Nonconvex Decentralized Nonlinear Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.19182 |