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On the Performance of NLP Solvers Within Global MINLP Solvers

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Operations Research Proceedings 2017

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.

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Notes

  1. 1.

    Solving Constraint Integer Programs, http://scip.zib.de.

  2. 2.

    Harwell Subroutine Library, http://www.hsl.rl.ac.uk.

  3. 3.

    MINLP Library 2, http://www.gamsworld.org/minlp/minlplib2.html.

  4. 4.

    H. Mittelmann MINLP Benchmark, http://plato.asu.edu/ftp/minlp.html.

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Acknowledgements

This work has been supported by the Research Campus MODAL Mathematical Optimization and Data Analysis Laboratories funded by the Federal Ministry of Education and Research (BMBF Grant 05M14ZAM).

Author information

Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Benjamin Müller

  2. University Bremen, Bibliothekstr. 5, 28195, Bremen, Germany

    Renke Kuhlmann

  3. GAMS Software GmbH, c/o Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Stefan Vigerske

Authors
  1. Benjamin Müller
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  2. Renke Kuhlmann
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  3. Stefan Vigerske
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Corresponding author

Correspondence to Benjamin Müller .

Editor information

Editors and Affiliations

  1. Department of Information Systems, Freie Universität Berlin, Berlin, Germany

    Natalia Kliewer

  2. Management Science Group, Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany

    Jan Fabian Ehmke

  3. Department of Mathematics, Freie Universität Berlin, Berlin, Germany

    Ralf Borndörfer

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Müller, B., Kuhlmann, R., Vigerske, S. (2018). On the Performance of NLP Solvers Within Global MINLP Solvers. In: Kliewer, N., Ehmke, J., Borndörfer, R. (eds) Operations Research Proceedings 2017. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-89920-6_84

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