State-constrained control-affine parabolic problems I: First and Second order necessary optimality conditions
Résumé
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 multidimen-sional. 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. The appendix provides an example illustrating the applicability of our results.
Domaines
Optimisation et contrôle [math.OC]| Origine | Fichiers produits par l'(les) auteur(s) |
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