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Journal Articles Set-Valued and Variational Analysis Year : 2020

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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Dates and versions

hal-03011004 , version 1 (17-11-2020)

Identifiers

  • HAL Id : hal-03011004 , version 1

Cite

M Soledad 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, In press. ⟨hal-03011004⟩
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