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-/sos-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-/sos-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.
This preprint has not undergone peer review (when applicable) or any post-submission improvements or corrections. The Version of Record of this article is published in Journal of Optimization Theory and Applications, and is available online at https://doi.org/10.1007/s10957-025-02631-6
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