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Granularity for Mixed-Integer Polynomial Optimization Problems

Author

Listed:
  • Carl Eggen

    (University of Konstanz)

  • Oliver Stein

    (Karlsruhe Institute of Technology (KIT))

  • Stefan Volkwein

    (University of Konstanz)

Abstract

Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sum-of-squares-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sum-of-squares-hierarchy is hereby used to solve those continuous polynomial problems, which generalizes known methods from the literature. Numerical examples from the MINLPLib illustrate our approach.

Suggested Citation

  • Carl Eggen & Oliver Stein & Stefan Volkwein, 2025. "Granularity for Mixed-Integer Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-24, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02631-6
    DOI: 10.1007/s10957-025-02631-6
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    References listed on IDEAS

    as
    1. Christoph Neumann & Oliver Stein & Nathan Sudermann-Merx, 2019. "A feasible rounding approach for mixed-integer optimization problems," Computational Optimization and Applications, Springer, vol. 72(2), pages 309-337, March.
    2. R. C. Jeroslow, 1973. "There Cannot be any Algorithm for Integer Programming with Quadratic Constraints," Operations Research, INFORMS, vol. 21(1), pages 221-224, February.
    3. Christoph Neumann & Oliver Stein & Nathan Sudermann-Merx, 2020. "Granularity in Nonlinear Mixed-Integer Optimization," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 433-465, February.
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