ALADIN-$β$: A Distributed Optimization Algorithm for Solving MPCC Problems
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918115920576512 |
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| author | Wang, Yifei Wu, Shuting Yang, Genke Chu, Jian Rikos, Apostolos I. Du, Xu |
| author_facet | Wang, Yifei Wu, Shuting Yang, Genke Chu, Jian Rikos, Apostolos I. Du, Xu |
| contents | Mathematical Programs with Complementarity Constraints (MPCC) are critical in various real-world applications but notoriously challenging due to non-smoothness and degeneracy from complementarity constraints. The $\ell_1$-Exact Penalty-Barrier enhanced \texttt{IPOPT} improves performance and robustness by introducing additional inequality constraints and decision variables. However, this comes at the cost of increased computational complexity due to the higher dimensionality and additional constraints introduced in the centralized formulation. To mitigate this, we propose a distributed structure-splitting reformulation that decomposes these inequality constraints and auxiliary variables into independent sub-problems. Furthermore, we introduce Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN)-$β$, a novel approach that integrates the $\ell_1$-Exact Penalty-Barrier method with ALADIN to efficiently solve the distributed reformulation. Numerical experiments demonstrate that even without a globalization strategy, the proposed distributed approach achieves fast convergence while maintaining high precision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ALADIN-$β$: A Distributed Optimization Algorithm for Solving MPCC Problems Wang, Yifei Wu, Shuting Yang, Genke Chu, Jian Rikos, Apostolos I. Du, Xu Systems and Control Mathematical Programs with Complementarity Constraints (MPCC) are critical in various real-world applications but notoriously challenging due to non-smoothness and degeneracy from complementarity constraints. The $\ell_1$-Exact Penalty-Barrier enhanced \texttt{IPOPT} improves performance and robustness by introducing additional inequality constraints and decision variables. However, this comes at the cost of increased computational complexity due to the higher dimensionality and additional constraints introduced in the centralized formulation. To mitigate this, we propose a distributed structure-splitting reformulation that decomposes these inequality constraints and auxiliary variables into independent sub-problems. Furthermore, we introduce Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN)-$β$, a novel approach that integrates the $\ell_1$-Exact Penalty-Barrier method with ALADIN to efficiently solve the distributed reformulation. Numerical experiments demonstrate that even without a globalization strategy, the proposed distributed approach achieves fast convergence while maintaining high precision. |
| title | ALADIN-$β$: A Distributed Optimization Algorithm for Solving MPCC Problems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2503.21502 |