Linear solvers for power grid optimization problems: a review of GPU-accelerated linear solvers

TL;DR

This paper reviews GPU-accelerated linear solvers for power grid optimization, benchmarking five packages on their accuracy and GPU performance, revealing limited acceleration and variable accuracy.

Contribution

It provides a comparative analysis of existing GPU-accelerated linear solvers applied to power grid optimization problems, highlighting their limitations.

Findings

Solution accuracy varies greatly among solvers.

No significant GPU acceleration was achieved.

Linear systems are challenging due to ill-conditioning.

Abstract

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDL^T decompositions. We benchmark five well known direct linear solver packages using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases.