{"ID":2868814,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.15938","arxiv_id":"2509.15938","title":"Enforcing Convergence in Sensitivity-based Distributed Programming via Transformed Primal-Dual Updates","abstract":"Sensitivity-based distributed programming (SBDP) is a decomposition method for solving large-scale nonlinear programs over graph-structured networks. However, its convergence depends on the strength and structure of subsystem coupling. To address this limitation, we propose SBDP+, a distributed optimization scheme based on a structured primal-dual operator design. The method employs first-order sensitivities and primal decomposition to construct low-dimensional local subproblems that are solved in parallel using neighbor-to-neighbor communication. In contrast to SBDP, SBDP+ introduces a novel primal-dual update that ensures convergence under general coupling structures. Specifically, we establish local linear convergence for non-convex problems under standard regularity conditions. Numerical experiments demonstrate the effectiveness of SBDP+ and highlight improved robustness compared to SBDP and representative distributed optimization methods in applications such as statistical learning.","short_abstract":"Sensitivity-based distributed programming (SBDP) is a decomposition method for solving large-scale nonlinear programs over graph-structured networks. However, its convergence depends on the strength and structure of subsystem coupling. To address this limitation, we propose SBDP+, a distributed optimization scheme base...","url_abs":"https://arxiv.org/abs/2509.15938","url_pdf":"https://arxiv.org/pdf/2509.15938v2","authors":"[\"Maximilian Pierer von Esch\",\"Andreas Völz\",\"Knut Graichen\"]","published":"2025-09-19T12:48:12Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}