GPU-accelerated dynamic nonlinear optimization with ExaModels and MadNLP

TL;DR

This paper demonstrates how GPU acceleration using ExaModels and MadNLP can significantly speed up large-scale dynamic nonlinear optimization problems, especially in solving sparse linear systems efficiently.

Contribution

It introduces a GPU-based approach for dynamic nonlinear optimization, combining automatic differentiation and hybrid linear solvers to achieve substantial speedups.

Findings

Reduced iteration time by a factor of 25 on a distillation column problem.

Hybrid solver effectively leverages GPU capabilities for sparse linear systems.

Pre-processing time remains significant but is offset by faster iterations.

Abstract

We investigate the potential of Graphics Processing Units (GPUs) to solve large-scale nonlinear programs with a dynamic structure. Using ExaModels, a GPU-accelerated automatic differentiation tool, and the interior-point solver MadNLP, we significantly reduce the time to solve dynamic nonlinear optimization problems. The sparse linear systems formulated in the interior-point method is solved on the GPU using a hybrid solver combining an iterative method with a sparse Cholesky factorization, which harness the newly released NVIDIA cuDSS solver. Our results on the classical distillation column instance show that despite a significant pre-processing time, the hybrid solver allows to reduce the time per iteration by a factor of 25 for the largest instance.