Scalable Mixed-Integer Optimization with Neural Constraints via Dual Decomposition
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911261726343168 |
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| author | Zeng, Shuli Zhang, Sijia Wu, Feng Tang, Shaojie Li, Xiang-Yang |
| author_facet | Zeng, Shuli Zhang, Sijia Wu, Feng Tang, Shaojie Li, Xiang-Yang |
| contents | Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this paper, we introduce a novel dual-decomposition framework that relaxes the single coupling equality u=x with an augmented Lagrange multiplier and splits the problem into a vanilla MIP and a constrained NN block. Each part is tackled by the solver that suits it best-branch and cut for the MIP subproblem, first-order optimisation for the NN subproblem-so the model remains modular, the number of integer variables never grows with network depth, and the per-iteration cost scales only linearly with the NN size. On the public \textsc{SurrogateLIB} benchmark, our method proves \textbf{scalable}, \textbf{modular}, and \textbf{adaptable}: it runs \(120\times\) faster than an exact Big-M formulation on the largest test case; the NN sub-solver can be swapped from a log-barrier interior step to a projected-gradient routine with no code changes and identical objective value; and swapping the MLP for an LSTM backbone still completes the full optimisation in 47s without any bespoke adaptation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Mixed-Integer Optimization with Neural Constraints via Dual Decomposition Zeng, Shuli Zhang, Sijia Wu, Feng Tang, Shaojie Li, Xiang-Yang Optimization and Control Machine Learning Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this paper, we introduce a novel dual-decomposition framework that relaxes the single coupling equality u=x with an augmented Lagrange multiplier and splits the problem into a vanilla MIP and a constrained NN block. Each part is tackled by the solver that suits it best-branch and cut for the MIP subproblem, first-order optimisation for the NN subproblem-so the model remains modular, the number of integer variables never grows with network depth, and the per-iteration cost scales only linearly with the NN size. On the public \textsc{SurrogateLIB} benchmark, our method proves \textbf{scalable}, \textbf{modular}, and \textbf{adaptable}: it runs \(120\times\) faster than an exact Big-M formulation on the largest test case; the NN sub-solver can be swapped from a log-barrier interior step to a projected-gradient routine with no code changes and identical objective value; and swapping the MLP for an LSTM backbone still completes the full optimisation in 47s without any bespoke adaptation. |
| title | Scalable Mixed-Integer Optimization with Neural Constraints via Dual Decomposition |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2511.09186 |