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One issue in many practical situations is that the follower\u2019s problem is not explicitly known by the leader. For such bilevel problems with unknown lower-level model we propose the use of neural networks to learn the follower\u2019s optimal response for given decisions of the leader based on available historical data of pairs of leader and follower decisions. Integrating the resulting neural network in a single-level reformulation of the bilevel problem leads to a challenging model with a black-box constraint. We exploit Lipschitz optimization techniques from the literature to solve this reformulation and illustrate the applicability of the proposed method with some preliminary case studies using academic and linear bilevel instances.<\/jats:p>","DOI":"10.1007\/s11590-022-01958-7","type":"journal-article","created":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T09:02:51Z","timestamp":1676538171000},"page":"1083-1103","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Using neural networks to solve linear bilevel problems with unknown lower level"],"prefix":"10.1007","volume":"17","author":[{"given":"Ioana","family":"Molan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6208-5677","authenticated-orcid":false,"given":"Martin","family":"Schmidt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,16]]},"reference":[{"issue":"1","key":"1958_CR1","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1002\/nav.3800310104","volume":"31","author":"JF Bard","year":"1984","unstructured":"Bard, J.F.: Optimality conditions for the bilevel programming problem. 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