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Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the main approach used to deal with the lower-level problem. Here, we utilize the concept of frontier map that extends the notion of optimal value function to our parametric multiobjective lower-level problem. Based on this, we build a tractable constraint qualification that we use to derive necessary optimality conditions for the problem. Subsequently, we show that our resulting necessary optimality conditions represent a natural extension from standard optimistic bilevel programs with scalar objective functions.\n<\/jats:p>","DOI":"10.1007\/s11590-022-01948-9","type":"journal-article","created":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T18:02:56Z","timestamp":1666980176000},"page":"1337-1358","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Extension of the value function reformulation to multiobjective bilevel optimization"],"prefix":"10.1007","volume":"17","author":[{"given":"Lahoussine","family":"Lafhim","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1265-4178","authenticated-orcid":false,"given":"Alain","family":"Zemkoho","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"1948_CR1","doi-asserted-by":"crossref","unstructured":"Arrow, K.J., Barankin, E.W., Blackwell, D.: Admissible points of convex sets, in Contributions to the Theory of Games, H. 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