Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [32 references]  Display  Hide  Download

https://hal.inria.fr/hal-03011004
Contributor : J. Frederic Bonnans <>
Submitted on : Tuesday, November 17, 2020 - 10:32:57 PM
Last modification on : Thursday, November 19, 2020 - 3:30:11 AM

File

ABKpart1_revision.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03011004, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

20

Files downloads

28