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We show finite termination and correctness of both methods and present extensive numerical results that illustrate the applicability of the approaches. It turns out that the proposed methods are capable of solving bilevel instances with several thousand variables and constraints and significantly outperform classical solution approaches.<\/jats:p>","DOI":"10.1007\/s10107-020-01601-2","type":"journal-article","created":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T12:39:11Z","timestamp":1612874351000},"page":"461-521","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Outer approximation for global optimization of mixed-integer quadratic bilevel problems"],"prefix":"10.1007","volume":"188","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7082-7466","authenticated-orcid":false,"given":"Thomas","family":"Kleinert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9025-9731","authenticated-orcid":false,"given":"Veronika","family":"Grimm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6208-5677","authenticated-orcid":false,"given":"Martin","family":"Schmidt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,2,8]]},"reference":[{"issue":"4","key":"1601_CR1","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1287\/ijoc.1090.0373","volume":"22","author":"K Abhishek","year":"2010","unstructured":"Abhishek, K., Leyffer, S., Linderoth, J.: FilMINT: an outer approximationbased solver for convex mixed-integer nonlinear programs. 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