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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.15938 |
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| _version_ | 1866918510609825792 |
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| author | von Esch, Maximilian Pierer Völz, Andreas Graichen, Knut |
| author_facet | von Esch, Maximilian Pierer Völz, Andreas Graichen, Knut |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enforcing Convergence in Sensitivity-based Distributed Programming via Transformed Primal-Dual Updates von Esch, Maximilian Pierer Völz, Andreas Graichen, Knut Optimization and Control 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. |
| title | Enforcing Convergence in Sensitivity-based Distributed Programming via Transformed Primal-Dual Updates |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.15938 |