Parallel Interior-Point Solver for Block-Structured Nonlinear Programs on SIMD/GPU Architectures

TL;DR

This paper presents a parallel interior-point method optimized for SIMD/GPU architectures to efficiently solve block-structured nonlinear programs, demonstrating significant speed-ups on exascale hardware.

Contribution

The paper introduces a two-level parallelization approach for interior-point methods tailored for SIMD/GPU architectures, reducing memory use and accelerating computations for large-scale nonlinear programs.

Findings

Achieves 50x speed-up over existing methods.

Effectively utilizes multi-GPU supercomputers for complex problems.

Demonstrates scalability on exascale architectures.

Abstract

We investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses a SIMD/GPU accelerator locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations, to a dense matrix encoding the sensitivities of the problem's degrees of freedom, drastically minimizing the memory exchange. We demonstrate the method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the method can achieve a 50x speed-up compared to the state-of-the-art method.