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

Kasia Świrydowicz; Eric Darve; Wesley Jones; Jonathan Maack; Shaked Regev; Michael A. Saunders; Stephen J. Thomas; Slaven Peleš

doi:10.1016/j.parco.2021.102870

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

Kasia Świrydowicz
, Eric Darve
, Wesley Jones
, Jonathan Maack
, Shaked Regev
, Michael A. Saunders
, Stephen J. Thomas
, Slaven Peleš

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they 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 on CPU- and GPU-based hardware, 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. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

Original language	English
Article number	102870
Journal	Parallel Computing
Volume	111
DOIs	https://doi.org/10.1016/j.parco.2021.102870
State	Published - Jul 2022
Externally published	Yes

Funding

This research was supported by the Exascale Computing Project ( 17-SC-20-SC ), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration . We thank Chris Oehmen and Lori Ross O’Neil for critical reading of the manuscript and helpful suggestions. We also thank Tim Carlson and Kurt Glaesmann of Research Computing for their support, as well as Kestor Gokcen and Jiajia Li for providing utilities for matrix format conversion (all from Pacific Northwest National Laboratory). Finally, we acknowledge the support from the Oak Ridge Leadership Computing Facility , in particular a great deal of help from Philip Roth. This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. We thank Chris Oehmen and Lori Ross O'Neil for critical reading of the manuscript and helpful suggestions. We also thank Tim Carlson and Kurt Glaesmann of Research Computing for their support, as well as Kestor Gokcen and Jiajia Li for providing utilities for matrix format conversion (all from Pacific Northwest National Laboratory). Finally, we acknowledge the support from the Oak Ridge Leadership Computing Facility, in particular a great deal of help from Philip Roth.

Keywords

GPU
Grid optimization
Solvers
Sparse linear equations

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title = "Linear solvers for power grid optimization problems: A review of GPU-accelerated linear solvers",

abstract = "The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDLT decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, 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. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.",

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AU - Świrydowicz, Kasia

AU - Darve, Eric

AU - Jones, Wesley

AU - Maack, Jonathan

AU - Regev, Shaked

AU - Saunders, Michael A.

AU - Thomas, Stephen J.

AU - Peleš, Slaven

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N2 - The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDLT decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, 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. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

AB - The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDLT decompositions. We benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, 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. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

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KW - Grid optimization

KW - Solvers

KW - Sparse linear equations

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JO - Parallel Computing

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ER -

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

Abstract

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Keywords

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