{"ID":2837607,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.19182","arxiv_id":"2511.19182","title":"A Unified Algorithm for Nonconvex Decentralized Nonlinear Optimization","abstract":"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.","short_abstract":"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 tr...","url_abs":"https://arxiv.org/abs/2511.19182","url_pdf":"https://arxiv.org/pdf/2511.19182v3","authors":"[\"Hao Wu\",\"Liping Wang\"]","published":"2025-11-24T14:50:21Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}