# GPU-accelerated dynamic nonlinear optimization with ExaModels and MadNLP

arXiv: https://arxiv.org/abs/2403.15913 · HTML: https://mlsanity.com/paper/2403.15913/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2024.

## Built on by (most cited first, 3 of 3)

- [Nonlinear Optimization with GPU-Accelerated Neural Network Constraints](https://mlsanity.com/paper/2509.22462/) (2025)
- [LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization](https://mlsanity.com/paper/2606.08993/) (2026)
- [SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling](https://mlsanity.com/paper/2607.00095/) (2026)

## Abstract (arXiv)

We investigate the potential of Graphics Processing Units (GPUs) to solve large-scale nonlinear programs with a dynamic structure. Using ExaModels, a GPU-accelerated automatic differentiation tool, and the interior-point solver MadNLP, we significantly reduce the time to solve dynamic nonlinear optimization problems. The sparse linear systems formulated in the interior-point method is solved on the GPU using a hybrid solver combining an iterative method with a sparse Cholesky factorization, which harness the newly released NVIDIA cuDSS solver. Our results on the classical distillation column instance show that despite a significant pre-processing time, the hybrid solver allows to reduce the time per iteration by a factor of 25 for the largest instance.