On the Existence of Lagrange Multipliers in Distribution Network Reconfiguration Problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916729570983936 |
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| author | Liu, Rong-Peng Song, Yue Wang, Xiaozhe Zeng, Bo |
| author_facet | Liu, Rong-Peng Song, Yue Wang, Xiaozhe Zeng, Bo |
| contents | Distribution network reconfiguration (DNR) is an effective approach for optimizing distribution network operation. However, the DNR problem is computationally challenging due to the mixed-integer non-convex nature. One feasible approach for addressing this challenge is to reformulate binary line on/off state variables as (continuous) non-convex constraints, leading to a nonconvex program. Unfortunately, it remains unclear whether this formulation satisfies the Karush-Kuhn-Tucker (KKT) conditions at locally optimal solutions. In this brief, we study the existence of Lagrange multipliers in DNR problems and prove that under mild assumptions, Lagrange multipliers exist for the DNR model at every locally optimal solution almost surely such that the KKT conditions hold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_06488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Existence of Lagrange Multipliers in Distribution Network Reconfiguration Problems Liu, Rong-Peng Song, Yue Wang, Xiaozhe Zeng, Bo Optimization and Control Systems and Control Distribution network reconfiguration (DNR) is an effective approach for optimizing distribution network operation. However, the DNR problem is computationally challenging due to the mixed-integer non-convex nature. One feasible approach for addressing this challenge is to reformulate binary line on/off state variables as (continuous) non-convex constraints, leading to a nonconvex program. Unfortunately, it remains unclear whether this formulation satisfies the Karush-Kuhn-Tucker (KKT) conditions at locally optimal solutions. In this brief, we study the existence of Lagrange multipliers in DNR problems and prove that under mild assumptions, Lagrange multipliers exist for the DNR model at every locally optimal solution almost surely such that the KKT conditions hold. |
| title | On the Existence of Lagrange Multipliers in Distribution Network Reconfiguration Problems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.06488 |