{"ID":2846078,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.02283","arxiv_id":"2511.02283","title":"Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence","abstract":"Motivated by the pervasive lack of privacy protection in existing distributed nonconvex optimization methods, this paper proposes a decentralized proximal primal-dual algorithm enabling double protection of privacy ($\\text{DPP}^2$) for minimizing nonconvex sum-utility functions over multi-agent networks, which ensures zero leakage of critical local information during inter-agent communications. We develop a two-tier privacy protection mechanism that first merges the primal and dual variables by means of a variable transformation, followed by embedding an additional random perturbation to further obfuscate the transmitted information. We theoretically establish that $\\text{DPP}^2$ ensures differential privacy for local objectives while achieving exact convergence under nonconvex settings. Specifically, $\\text{DPP}^2$ converges sublinearly to a stationary point and attains a linear convergence rate under the additional Polyak-Łojasiewicz (P-Ł) condition. Finally, a numerical example demonstrates the superiority of $\\text{DPP}^2$ over a number of state-of-the-art algorithms, showcasing the faster, exact convergence achieved by $\\text{DPP}^2$ under the same level of differential privacy.","short_abstract":"Motivated by the pervasive lack of privacy protection in existing distributed nonconvex optimization methods, this paper proposes a decentralized proximal primal-dual algorithm enabling double protection of privacy ($\\text{DPP}^2$) for minimizing nonconvex sum-utility functions over multi-agent networks, which ensures...","url_abs":"https://arxiv.org/abs/2511.02283","url_pdf":"https://arxiv.org/pdf/2511.02283v1","authors":"[\"Zichong Ou\",\"Dandan Wang\",\"Zixuan Liu\",\"Jie Lu\"]","published":"2025-11-04T05:51:34Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}