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Subject: second order analysis ×

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    State-constrained control-affine parabolic problems II: Second order sufficient optimality conditions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Aronna, M. Soledad; Bonnans, J. Frédéric; Kröner, Axel
    In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform.
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    State-constrained control-affine parabolic problems I: First and second order necessary optimality conditions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Aronna, M. Soledad; Bonnans, J. Frédéric; Kröner, Axel
    In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions.