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State-constrained control-affine parabolic problems I: First and Second order necessary optimality conditions

Abstract : 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.
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https://hal.inria.fr/hal-03011004
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Submitted on : Tuesday, November 17, 2020 - 10:32:57 PM
Last modification on : Wednesday, November 3, 2021 - 9:54:25 AM
Long-term archiving on: : Thursday, February 18, 2021 - 8:34:11 PM

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  • HAL Id : hal-03011004, version 1

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M Aronna, J. Frederic Bonnans, Axel Kröner. State-constrained control-affine parabolic problems I: First and Second order necessary optimality conditions. Set-Valued and Variational Analysis, Springer, In press. ⟨hal-03011004⟩

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