Year: 2025
Type: article
Abstract: This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not only linearly but also as the argument of a regularization of the Heaviside function. The non-linearity which acts on the state is locally Lipschitz-continuous and not necessarily differentiable, i.e., non-smooth. This excludes the application of standard adjoint calculus. We derive conditions under which a strong stationary optimality system can be established, i.e., a system that is equivalent to the purely primal optimality condition saying that the directional derivative of the reduced objective in feasible directions is nonnegative. For this, two assumptions are made on the unknown optimizer. Some of the presented findings are employed in the recent contribution [8], where limit optimality systems for non-smooth shape optimization problems [7] are established.
DOI: 10.3934/mcrf.2025032
Author: Livia Betz
Institution: University of Würzburg
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
Award: G1635304455
OpenAlex ID: W4410865365