MathOptAI.jl: Embed Trained Machine-Learning Predictors into JuMP Models

References

• Albersmeyer J, Diehl M (2010) The lifted newton method and its application in optimization. SIAM J. Optim. 20(3):1655–1684.Crossref, Google Scholar
• Bates D, Noack A, Kornblith S, Bouchet-Valat M, Borregaard MK, Arslan A, White JM, et al. (2023) JuliaStats/GLM.jl, version 1.9.0. Accessed March 22, 2026, http://dx.doi.org/10.5281/zenodo.8345558.Google Scholar
• Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1):65–98.Crossref, Google Scholar
• Bolusani S, Besançon M, Bestuzheva K, Chmiela A, Dionísio J, Donkiewicz T, van Doornmalen J, et al. (2024) The SCIP optimization suite 9.0. Preprint, submitted February 27, https://arxiv.org/abs/2402.17702.Google Scholar
• Bynum ML, Hackebeil GA, Hart WE, Laird CD, Nicholson BL, Siirola JD, Watson JP, Woodruff DL (2021) Pyomo–Optimization Modeling in Python, vol. 67, 2nd ed. (Springer Science & Business Media, Cham, Switzerland).Crossref, Google Scholar
• Casas CAE (2024) Robust NMPC of large-scale systems and surrogate embedding strategies for NMPC. Masters thesis, University of Waterloo, Waterloo, ON.Google Scholar
• Casas CAE, Ricardez-Sandoval LA, Pulsipher JL (2025) A comparison of strategies to embed physics-informed neural networks in nonlinear model predictive control formulations solved via direct transcription. Comput. Chemical Engrg. 198:109105.Crossref, Google Scholar
• Ceccon F, Jalving J, Haddad J, Thebelt A, Tsay C, Laird CD, Misener R (2022) OMLT: Optimization & machine learning toolkit. J. Machine Learn. Res. 23(349):1–8.Google Scholar
• Dowson O, Parker RB, Bent R (2026) MathOptAI.jl: Embed trained machine-learning predictors into JuMP models. https://doi.org/10.1287/ijoc.2025.1446.cd, https://github.com/INFORMSJoC/2025.1446.Google Scholar
• GAMS Development Corporation (2026) GAMSPy: Algebraic modeling interface to GAMS. Accessed January 1, 2026, https://github.com/GAMS-dev/gamspy.Google Scholar
• Gurobi Optimization, LLC (2026a) Gurobi machine learning. Accessed January 1, 2026, https://github.com/Gurobi/gurobi-machinelearning.Google Scholar
• Gurobi Optimization, LLC (2026b) Gurobi optimizer. Accessed January 1, 2026, https://www.gurobi.com.Google Scholar
• Huangfu Q, Hall JAJ (2018) Parallelizing the dual revised simplex method. Math. Program. Comput. 10(1):119–142.Crossref, Google Scholar
• Innes M (2018) Flux: Elegant machine learning with Julia. J. Open Source Software 3(25):602.Crossref, Google Scholar
• Legat B, Dowson O, Dias Garcia J, Lubin M (2021) MathOptInterface: A data structure for mathematical optimization problems. INFORMS J. Comput. 34(2):672–689.Link, Google Scholar
• López-Flores FJ, Ramírez-Márquez C, Ponce-Ortega JM (2024) Process systems engineering tools for optimization of trained machine learning models: Comparative and perspective. Indust. Engrg. Chemistry Res. 63(32):13966–13979.Crossref, Google Scholar
• Lubin M, Dowson O, Garcia JD, Huchette J, Legat B, Vielma JP (2023) JuMP 1.0: Recent improvements to a modeling language for mathematical optimization. Math. Programming Comput. 15(3):581–589.Crossref, Google Scholar
• Pal A (2023) Lux: Explicit parameterization of deep neural networks in Julia, Version 0.5.0. Accessed March 22, 2026, http://dx.doi.org/10.5281/zenodo.7808904.Google Scholar
• Parker RB, Dowson O, LoGiudice N, Garcia M, Bent R (2025) Nonlinear optimization with GPU-accelerated neural network constraints. ScaleOPT: NeurIPS 2025 Workshop on GPU-Accelerated and Scalable Optimization, https://arxiv.org/abs/2509.22462.Google Scholar
• Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, et al. (2019) Pytorch: An imperative style, high-performance deep learning library. Adv. Neural Inform. Processing Systems 32:8024–8035.Google Scholar
• Sadeghi B, Chiarawongse P, Squire K, Jones DC, Noack A, St-Jean C, Huijzer R, et al. (2022) DecisionTree.jl—A Julia implementation of the CART Decision Tree and Random Forest algorithms, Version 0.11.3. Accessed March 22, 2026, http://dx.doi.org/10.5281/zenodo.7359268.Google Scholar
• Turner M, Chmiela A, Koch T, Winkler M (2025) PySCIPOpt-ML: Embedding trained machine learning models into mixed-integer programs. Tack G, ed. Integration of Constraint Programming, Artificial Intelligence, and Operations Research (Springer Nature Switzerland Cham, Switzerland), 218–234.Crossref, Google Scholar
• Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programming 106(1):25–57.Crossref, Google Scholar