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Characterization of a local quadratic growth of the Hamiltonian for control constrained optimal control problems. (English) Zbl 1264.49020

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.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
90C46 Optimality conditions and duality in mathematical programming
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