HyKKT: a hybrid direct-iterative method for solving KKT linear systems

We propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the...

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Vydáno v:Optimization methods & software Ročník 38; číslo 2; s. 332 - 355
Hlavní autoři: Regev, Shaked, Chiang, Nai-Yuan, Darve, Eric, Petra, Cosmin G., Saunders, Michael A., Świrydowicz, Kasia, Peleš, Slaven
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 04.03.2023
Taylor & Francis Ltd
Témata:
Cholesky factorization
Factorization
GPU
Graphics processing units
interior methods
KKT systems
Linear systems
MATHEMATICS AND COMPUTING
Optimization
Performance degradation
Power flow
sparse matrix factorization
ISSN:1055-6788, 1029-4937
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Shrnutí:We propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where is a lower triangular matrix and is or block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
PNNL-SA-166808
USDOE Office of Science (SC)
AC05-76RL01830
USDOE National Nuclear Security Administration (NNSA)
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2022.2124990