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To simplify the problem at hand, we convert it into a single-level optimal control problem by mapping the solution set of the quasi-variational inequality to a parametric optimization problem and employing the value function reformulation. Furthermore, we introduce certain regularity conditions to ensure that the derived maximum principle remains non-degenerate. Finally, we provide an illustrative example to elucidate our research findings.<\/jats:p>","DOI":"10.1051\/ro\/2024065","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T19:59:42Z","timestamp":1709927982000},"page":"1789-1805","source":"Crossref","is-referenced-by-count":1,"title":["Optimality conditions for bilevel optimal control problems with non-convex quasi-variational inequalities"],"prefix":"10.1051","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5502-2210","authenticated-orcid":false,"given":"Rachid","family":"El Idrissi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4589-4346","authenticated-orcid":false,"given":"Lahoussine","family":"Lafhim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1434-2541","authenticated-orcid":false,"given":"El Mostafa","family":"Kalmoun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4117-052X","authenticated-orcid":false,"given":"Youssef","family":"Ouakrim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,4,16]]},"reference":[{"key":"R1","unstructured":"Adams R.A. and Fournier J.J., Sobolev Spaces. 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