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arXiv · 2509.22462

Nonlinear Optimization with GPU-Accelerated Neural Network Constraints

Robert Parker·Oscar Dowson·Nicole LoGiudice·Manuel Garcia·Russell Bent
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Abstract

We propose a reduced-space formulation for optimizing over trained neural networks where the network's outputs and derivatives are evaluated on a GPU. To do this, we treat the neural network as a "gray box" where intermediate variables and constraints are not exposed to the optimization solver. Compared to the full-space formulation, in which intermediate variables and constraints are exposed to the optimization solver, the reduced-space formulation leads to faster solves and fewer iterations in an interior point method. We demonstrate the benefits of this method on two optimization problems: Adversarial generation for a classifier trained on MNIST images and security-constrained optimal power flow with transient feasibility enforced using a neural network surrogate.

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Robert Parker, Oscar Dowson, Nicole LoGiudice, Manuel Garcia, Russell Bent. 2025-09-26. Nonlinear Optimization with GPU-Accelerated Neural Network Constraints. https://arxiv.org/abs/2509.22462

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