First- and second-order optimality conditions for a strong local minimum in control problems with pure state constraints (Q2372172)

This paper proves the result announced by the authors in [\textit{Z. Páles} and \textit{V. Zeidan}, J. Glob. Optim. 28, No. 3--4, 363--377 (2004; Zbl 1152.49310)]: a necessary optimality condition for strong local minimum of optimal control problems with pure state set-inclusion constraints. The proof of the result is based on the Dubovitskii-Milyutin time transformation [\textit{A. Ya. Dubovitskii} and \textit{A. A. Milyutin}, Sov. Math., Dokl. 4, 452--455 (1963); translation from Dokl. Akad. Nauk SSSR 149, 759--762 (1963; Zbl 0133.05501)].