mlsanityData to 7 Oct 2026

Global Deterministic Optimization with Artificial Neural Networks Embedded

arXiv 1801.07114 ↗First posted 22 Jan 2018math.OCcited by 32

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Abstract (arXiv)

Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [textitSIOPT, 20 (2009), pp. 573-601] including the convex and concave envelopes of the nonlinear activation function of ANNs. The optimization problem is solved using our in-house global deterministic solver MAiNGO. The performance of the proposed method is shown in four optimization examples: an illustrative function, a fermentation process, a compressor plant and a chemical process optimization. The results show that computational solution time is favorable compared to the global general-purpose optimization solver BARON.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Jan 2018.

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Citing papers per year: 2021: 4; 2022: 9; 2023: 4; 2024: 4; 2025: 8; 2026: 3.

32 papers.

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  1. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  2. 2022OMLT: Optimization & Machine Learning Toolkitcited by 34
  3. 2021Mixed-Integer Optimization with Constraint Learningcited by 30
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  5. 2021Optimization with Constraint Learning: A Framework and Surveycited by 28
  6. 2022Maximizing information from chemical engineering data sets: Applications to machine learningcited by 17
  7. 2022TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learningcited by 15
  8. 2025ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projectioncited by 15
  9. 2022Learning from flowsheets: A generative transformer model for autocompletion of flowsheetscited by 10
  10. 2021Modeling Design and Control Problems Involving Neural Network Surrogatescited by 8
  11. 2022Counterfactual Explanations Using Optimization With Constraint Learningcited by 8
  12. 2023PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programscited by 8
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  5. 2025Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?cited by 3
  6. 2025An analysis of optimization problems involving ReLU neural networkscited by 2
  7. 2025Federated Learning from Molecules to Processes: A Perspectivecited by 2
  8. 2021Optimizing over an ensemble of neural networkscited by 1
  9. 2022Constraint Learning to Define Trust Regions in Predictive-Model Embedded Optimizationcited by 1
  10. 2022Digital Twin and Artificial Intelligence Incorporated With Surrogate Modeling for Hybrid and Sustainable Energy Systemscited by 1
  11. 2023Physics Informed Piecewise Linear Neural Networks for Process Optimizationcited by 1
  12. 2024Formulations and scalability of neural network surrogates in nonlinear optimization problemscited by 1
  13. 2025Nonlinear Optimization with GPU-Accelerated Neural Network Constraintscited by 1
  14. 2026Relaxation-Informed Training of Neural Network Surrogate Modelscited by 1
  15. 2024Tightening convex relaxations of trained neural networks: a unified approach for convex and S-shaped activationscited by 0
  16. 2025A physics-informed Bayesian optimization method for rapid development of electrical machinescited by 0
  17. 2025Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogatecited by 0
  18. 2025Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparisoncited by 0
  19. 2026Data-Driven Conditional Flexibility Indexcited by 0
  20. 2026Representation Learning for Exact Preimagescited by 0