Volume 28, 2022
|Number of page(s)||30|
|Published online||23 December 2022|
Stability in Affine Optimal Control Problems Constrained by Semilinear Elliptic Partial Differential Equations*
Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology,
** Corresponding author: email@example.com
Accepted: 8 November 2022
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping associated with the system of first order necessary optimality conditions. Preliminary results concerning the differentiability of the functions involved are established, especially the so-called switching function. Using this ansatz, more general nonlinear perturbations are encompassed, and under weaker assumptions than the ones previously considered in the literature on control constrained elliptic problems. Finally, the applicability of the results is illustrated with some error estimates for the Tikhonov regularization.
Mathematics Subject Classification: 35J60 / 49J20 / 49K20 / 49K40
Key words: Semilinear elliptic equations / stability analysis / metric subregularity / optimality mapping / optimality conditions / Tikhonov regularization
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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