# Optimization with Trained Machine Learning Models Embedded

arXiv: https://arxiv.org/abs/2207.12722 · HTML: https://mlsanity.com/paper/2207.12722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Scaling up machine learning-based chemical plant simulation: A method for fine-tuning a model to induce stable fixed points](https://mlsanity.com/paper/2307.13621/) (2023)
- [An Efficient Spatial Branch-and-Bound Algorithm for Global Optimization of Gaussian Process Posterior Mean Functions](https://mlsanity.com/paper/2605.00855/) (2026)

## Abstract (arXiv)

Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit homogeneous structures and repeating patterns (e.g., layers in ANNs). Thus, specialized solution strategies can be used for large problem classes. Recently, there have been some promising works proposing specialized reformulations using mixed-integer programming or reduced space formulations. However, further work is needed to develop more efficient solution approaches and keep up with the rapid development of new ML model architectures.