Second order analysis of state-constrained control-affine problems

Abstract : In this article we establish new second order necessary and suffi-cient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.
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Maria Soledad Aronna, J. Frederic Bonnans, Bean San Goh. Second order analysis of state-constrained control-affine problems. Mathematical Programming, Series A, Springer, 2016, 160 (1), pp.115-147. ⟨hal-01081111v2⟩

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