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.
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Acknowledgements
This work is funded by the Federal Ministry for Economic Affairs and Energy within the BEAM-MEproject (ID: 03ET4023A-F) and by the Federal Ministry of Education and Research within the Research Campus MODAL(ID : 05M14ZAM). The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time through the John von Neumann Institute for Computing (NIC ) on the GCS Supercomputer JUWELSat Jülich Supercomputing Centre (JSC ).
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Gleixner, A., Kempke, NC., Koch, T., Rehfeldt, D., Uslu, S. (2020). First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method. In: Neufeld, J.S., Buscher, U., Lasch, R., Möst, D., Schönberger, J. (eds) Operations Research Proceedings 2019. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-48439-2_13
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DOI: https://doi.org/10.1007/978-3-030-48439-2_13
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