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

In: Operations Research Proceedings 2019

Author

Listed:
  • Ambros Gleixner

    (Zuse Institute Berlin)

  • Nils-Christian Kempke

    (Zuse Institute Berlin)

  • Thorsten Koch

    (Zuse Institute Berlin
    Technische Universität Berlin)

  • Daniel Rehfeldt

    (Zuse Institute Berlin
    Technische Universität Berlin)

  • Svenja Uslu

    (Zuse Institute Berlin)

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.

Suggested Citation

  • Ambros Gleixner & Nils-Christian Kempke & Thorsten Koch & Daniel Rehfeldt & Svenja Uslu, 2020. "First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 105-111, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_13
    DOI: 10.1007/978-3-030-48439-2_13
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