{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T02:54:41Z","timestamp":1787367281958,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>In this article, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima.<\/jats:p>","DOI":"10.1137\/130923452","type":"journal-article","created":{"date-parts":[[2014,12,10]],"date-time":"2014-12-10T13:31:34Z","timestamp":1418218294000},"page":"3887-3916","source":"Crossref","is-referenced-by-count":16,"title":["Second-Order Necessary Conditions in Pontryagin Form for Optimal Control Problems"],"prefix":"10.1137","volume":"52","author":[{"given":"J. Fr\u00e9d\u00e9ric","family":"Bonnans","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xavier","family":"Dupuis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laurent","family":"Pfeiffer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,12,10]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"L. Ambrosio, N. Fusco, and D. Pallara,\n                      Functions of Bounded Variation and Free Discontinuity Problems\n                      , Oxford Math. Monogr., Oxford University Press, New York, 2000.","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-013-0299-3"},{"key":"atypb3","unstructured":"J. F. Bonnans, X. Dupuis, and L. 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