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This paper introduces a novel computational framework for solving alternatingcurrent optimal power flow (ACOPF) problems using graphics processing units(GPUs). While GPUs have demonstrated remarkable performance in variouscomputing domains, their application in AC OPF has been limited due tochallenges associated with porting sparse automatic differentiation (AD) andsparse linear solver routines to GPUs. We aim to address these issues with twokey strategies. First, we utilize a single-instruction, multiple-data (SIMD)abstraction of nonlinear programs (NLP). This approach enables thespecification of model equations while preserving their parallelizablestructure, and in turn, facilitates the implementation of AD routines that canexploit such structure. Second, we employ a condensed-space interior-pointmethod (IPM) with an inequality relaxation strategy. This technique involvesrelaxing equality constraints to inequalities and condensing theKarush-Kuhn-Tucker system into a much smaller positive definite system. Thisstrategy offers the key advantage of being able to factorize the KKT matrixwithout numerical pivoting, which in the past has hampered the parallelizationof the IPM algorithm. By combining these two strategies, we can perform themajority of operations on GPUs while keeping the data residing in the devicememory only. Comprehensive numerical benchmark results showcase the substantialcomputational advantage of our approach. Remarkably, for solving large-scale ACOPF problems to a moderate accuracy, our implementations -- MadNLP.jl andExaModels.jl -- running on NVIDIA GPUs achieve an order of magnitude speedupcompared to state-of-the-art tools running on contemporary CPUs.

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