First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method

Ambros Gleixner, Nils-Christian Kempke (), Thorsten Koch, Daniel Rehfeldt and Svenja Uslu
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Ambros Gleixner: Zuse Institute Berlin
Nils-Christian Kempke: Zuse Institute Berlin
Thorsten Koch: Zuse Institute Berlin
Daniel Rehfeldt: Zuse Institute Berlin
Svenja Uslu: Zuse Institute Berlin

A chapter in Operations Research Proceedings 2019, 2020, pp 105-111 from Springer

Abstract: Abstract In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.

Keywords: Block structure; Energy system models; HPC; Linear programming; Interior-point methods; Parallelization; Presolving (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-030-48439-2_13

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DOI: 10.1007/978-3-030-48439-2_13

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