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Our approach also provides a new and unified calibrated formulation of the appropriate constraint qualifications, and shows how to extend them to nonsmooth data. Other features include a very weak hypothesis concerning the type of local minimum, nonrestrictive hypotheses on the data, and stronger conclusions, notably as regards the maximum (or Weierstrass) condition. The necessary conditions are stratified, in the sense that they are asserted on precisely the domain upon which the hypotheses (and the optimality) are assumed to hold. This leads to local, intermediate, and global versions of the necessary conditions, according to how the hypotheses are formulated.<\/jats:p>","DOI":"10.1137\/090757642","type":"journal-article","created":{"date-parts":[[2010,8,5]],"date-time":"2010-08-05T18:13:42Z","timestamp":1281032022000},"page":"4500-4524","source":"Crossref","is-referenced-by-count":71,"title":["Optimal Control Problems with Mixed Constraints"],"prefix":"10.1137","volume":"48","author":[{"given":"Francis","family":"Clarke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. R.","family":"de Pinho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,8,5]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"A. V. Arutyunov,\n                      Optimality Conditions. 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Milyutin,\n                      Theory of the principle of the maximum\n                      , in Methods of the Theory of Extremal Problems in Economics, Nauka, Moscow, 1981, pp. 7\u201347."},{"key":"R22","first-page":"315","volume":"24","author":"Gamkrelidze R. V.","year":"1960","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat.","ISSN":"https:\/\/id.crossref.org\/issn\/0373-2436","issn-type":"print"},{"key":"R23","unstructured":"M. R. Hestenes,\n                      Calculus of Variations and Optimal Control Theory\n                      , John Wiley & Sons, New York, 1966."},{"key":"R24","doi-asserted-by":"crossref","unstructured":"A. D. Ioffe and R. T. Rockafellar,\n                      The Euler and Weierstrass conditions for nonsmooth variational problems\n                      , Calc. Var. Partial Differential Equations, 4 (1996). pp. 59\u201387.","DOI":"10.1007\/BF01322309"},{"key":"R25","unstructured":"A. D. Ioffe and V. M. 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