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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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