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We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard, computing feasible iterates via calls to a generic mixed-integer linear solver. Convergence to critical, possibly suboptimal, feasible points is established for arbitrary starting points. Finally, we present numerical applications in nonsmooth optimal control and optimal network design and operation.<\/jats:p>","DOI":"10.1007\/s11590-025-02190-9","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T04:33:14Z","timestamp":1740544394000},"page":"1883-1904","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Mixed-integer linearity in nonlinear optimization: a trust region approach"],"prefix":"10.1007","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3545-6898","authenticated-orcid":false,"given":"Alberto","family":"De Marchi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"2190_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492913000032","volume":"22","author":"P Belotti","year":"2013","unstructured":"Belotti, P., Kirches, C., Leyffer, S., Linderoth, J., Luedtke, J., Mahajan, A.: Mixed-integer nonlinear optimization. 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