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Both Karush\u2013Kuhn\u2013Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond\u2013Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.<\/jats:p>","DOI":"10.1007\/s10288-021-00482-1","type":"journal-article","created":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T21:02:50Z","timestamp":1622754170000},"page":"417-442","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Optimality conditions and Mond\u2013Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2218-7668","authenticated-orcid":false,"given":"Tadeusz","family":"Antczak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"key":"482_CR1","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10107-006-0083-3","volume":"114","author":"W Achtziger","year":"2008","unstructured":"Achtziger W, Kanzow C (2008) Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. 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