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Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II

Author

Listed:
  • Benjamin Beach

    (Virginia Tech)

  • Robert Burlacu

    (Fraunhofer Institute for Integrated Circuits IIS)

  • Andreas Bärmann

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

  • Lukas Hager

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

  • Robert Hildebrand

    (Virginia Tech)

Abstract

This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver.

Suggested Citation

  • Benjamin Beach & Robert Burlacu & Andreas Bärmann & Lukas Hager & Robert Hildebrand, 2024. "Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II," Computational Optimization and Applications, Springer, vol. 87(3), pages 893-934, April.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:3:d:10.1007_s10589-024-00554-y
    DOI: 10.1007/s10589-024-00554-y
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    References listed on IDEAS

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    1. Benjamin Beach & Robert Hildebrand & Joey Huchette, 2022. "Compact mixed-integer programming formulations in quadratic optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 869-912, December.
    2. Kevin-Martin Aigner & Robert Burlacu & Frauke Liers & Alexander Martin, 2023. "Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 458-474, March.
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    1. Benjamin Beach & Robert Burlacu & Andreas Bärmann & Lukas Hager & Robert Hildebrand, 2024. "Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part I," Computational Optimization and Applications, Springer, vol. 87(3), pages 835-891, April.

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