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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.<\/jats:p>","DOI":"10.1007\/s10957-025-02631-6","type":"journal-article","created":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T12:51:39Z","timestamp":1741265499000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Granularity for Mixed-Integer Polynomial Optimization Problems"],"prefix":"10.1007","volume":"205","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-0753-2547","authenticated-orcid":false,"given":"Carl","family":"Eggen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"Stein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Volkwein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,6]]},"reference":[{"key":"2631_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-6328-5","volume-title":"Non-Linear Parametric Optimization","author":"B Bank","year":"1982","unstructured":"Bank, B., Guddat, J., Klatte, D., Kummer, B., Tammer, K.: Non-Linear Parametric Optimization. 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