Condensed-space methods for nonlinear programming on GPUs
Résumé
This paper explores two condensed-space interior-point methods to efficiently solve large-scale nonlinear programs on graphics processing units (GPUs). The interior-point method solves a sequence of symmetric indefinite linear systems, or Karush-Kuhn-Tucker (KKT) systems, which become increasingly ill-conditioned as we approach the solution. Solving a KKT system with traditional sparse factorization methods involve numerical pivoting, making parallelization difficult. A solution is to condense the KKT system into a symmetric positive-definite matrix and solve it with a Cholesky factorization, stable without pivoting. Although condensed KKT systems are more prone to ill-conditioning than the original ones, they exhibit structured ill-conditioning that mitigates the loss of accuracy. This paper compares the benefits of two recent condensed-space interior-point methods, HyKKT and LiftedKKT. We implement the two methods on GPUs using MadNLP.jl, an optimization solver interfaced with the NVIDIA sparse linear solver cuDSS and with the GPUaccelerated modeler ExaModels.jl. Our experiments on the PGLIB and the COPS benchmarks reveal that GPUs can attain up to a tenfold speed increase compared to CPUs when solving large-scale instances.
Domaines
Optimisation et contrôle [math.OC]Origine | Fichiers produits par l'(les) auteur(s) |
---|