# Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods

arXiv: https://arxiv.org/abs/2307.16830 · HTML: https://mlsanity.com/paper/2307.16830/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2023.

## Built on by (most cited first, 11 of 11)

- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation](https://mlsanity.com/paper/2501.17737/) (2025)
- [A General and Streamlined Differentiable Optimization Framework](https://mlsanity.com/paper/2510.25986/) (2025)
- [Sobolev Training of End-to-End Optimization Proxies](https://mlsanity.com/paper/2505.11342/) (2025)
- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [Differentiable Optimization for Deep Learning-Enhanced DC Approximation of AC Optimal Power Flow](https://mlsanity.com/paper/2504.01970/) (2025)
- [Nonlinear Optimization with GPU-Accelerated Neural Network Constraints](https://mlsanity.com/paper/2509.22462/) (2025)
- [Generating adversarial inputs for a graph neural network model of AC power flow](https://mlsanity.com/paper/2602.17975/) (2026)
- [SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling](https://mlsanity.com/paper/2607.00095/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)

## Abstract (arXiv)

This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their application in ACOPF has been limited due to challenges associated with porting sparse automatic differentiation (AD) and sparse linear solver routines to GPUs. We address these issues with two key strategies. First, we utilize a single-instruction, multiple-data abstraction of nonlinear programs. This approach enables the specification of model equations while preserving their parallelizable structure and, in turn, facilitates the parallel AD implementation. Second, we employ a condensed-space interior-point method (IPM) with an inequality relaxation. This technique involves condensing the Karush--Kuhn--Tucker (KKT) system into a positive definite system. This strategy offers the key advantage of being able to factorize the KKT matrix without numerical pivoting, which has hampered the parallelization of the IPM algorithm. By combining these strategies, we can perform the majority of operations on GPUs while keeping the data residing in the device memory only. Comprehensive numerical benchmark results showcase the advantage of our approach. Remarkably, our implementations -- MadNLP.jl and ExaModels.jl -- running on NVIDIA GPUs achieve an order of magnitude speedup compared with state-of-the-art tools running on contemporary CPUs.