IAI-Veranstaltungskalender
A novel condensed-space interior-point method for nonlinear programming on GPUs
We present a novel interior-point method to solve nonlinear programs on graphical processing units (GPUs). The classical interior-point method solves a sequence of symmetric indefinite linear systems, or Karush-Kuhn-Tucker (KKT) systems, that are increasingly ill-conditioned as we approach the solution. Solving a KKT system with traditional sparse factorization methods involves numerical pivoting, making parallelization difficult. A remedy 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. We have implemented the condensed-space interior-point method on the GPU using MadNLP.jl, an optimization solver interfaced with the NVIDIA sparse linear solver cuDSS and with the GPU-accelerated modeler ExaModels.jl. Our experiments on large-scale OPF and optimal control instances reveal that GPUs can attain up to a tenfold speed increase compared to CPUs
https://www.iai.kit.edu
Prof. Dr. François Pacaud
Centre Automatique et Systèmes Ecole des Mines de Paris