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The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.<\/jats:p>","DOI":"10.1093\/imamci\/dnz036","type":"journal-article","created":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T15:12:48Z","timestamp":1571843568000},"page":"1021-1047","source":"Crossref","is-referenced-by-count":5,"title":["A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition"],"prefix":"10.1093","volume":"37","author":[{"given":"Roberto","family":"Andreani","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, State University of Campinas (Unicamp) , Rua S\u00e9rgio Buarque de Holanda, N. 651, CEP 13083-859, Campinas - SP, Brasil"}]},{"given":"Valeriano","family":"Antunes de Oliveira","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, S\u00e3o Paulo State University (Unesp) , Rua Crist\u00f3v\u00e3o Colombo, N. 2265, CEP 15054-000, S\u00e3o Jos\u00e9 do Rio Preto - SP, Brasil"}]},{"given":"Jamielli","family":"Tomaz Pereira","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, State University of Campinas (Unicamp) , Rua S\u00e9rgio Buarque de Holanda, N. 651, CEP 13083-859, Campinas - SP, Brasil"}]},{"given":"Geraldo","family":"Nunes Silva","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, S\u00e3o Paulo State University (Unesp) , Rua Crist\u00f3v\u00e3o Colombo, N. 2265, CEP 15054-000, S\u00e3o Jos\u00e9 do Rio Preto - SP, Brasil"}]}],"member":"286","published-online":{"date-parts":[[2020,2,5]]},"reference":[{"key":"2026041420060763600_ref1","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1137\/060654797","article-title":"On augmented Lagrangian methods with general lower-level constraints","volume":"18","author":"Andreani","year":"2007","journal-title":"SIAM J. 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