Bonnans, J. Frédéric; Osmolovskii, Nikolai P. Characterization of a local quadratic growth of the Hamiltonian for control constrained optimal control problems. (English) Zbl 1264.49020 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 19, No. 1-2, 1-16 (2012). Summary: We consider an optimal control problem with inequality control constraints given by smooth functions satisfying the hypothesis of linear independence of gradients of active constraints. For this problem, we formulate a generalization of the strengthened Legendre condition and prove that this generalization is equivalent to the condition of a local quadratic growth of the Hamiltonian subject to control constraints. Cited in 3 Documents MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 90C46 Optimality conditions and duality in mathematical programming Keywords:Pontryagin’s principle; Legendre condition; Hamiltonian; control constraints; quadratic growth; sufficient optimality conditions PDFBibTeX XMLCite \textit{J. F. Bonnans} and \textit{N. P. Osmolovskii}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 19, No. 1--2, 1--16 (2012; Zbl 1264.49020) Full Text: Link