Issue |
ESAIM: COCV
Volume 31, 2025
|
|
---|---|---|
Article Number | 1 | |
Number of page(s) | 37 | |
DOI | https://doi.org/10.1051/cocv/2024075 | |
Published online | 06 January 2025 |
Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control
1
Faculty of Mathematics, TU Dortmund University, 44227 Dortmund, Germany
2
Department of Mathematics, Radboud University, 6525 AJ Nijmegen, The Netherlands
* Corresponding author: paul.manns@tu-dortmund.de
Received:
19
October
2023
Accepted:
19
September
2024
We consider optimal control problems that have binary-valued control input functions and a perimeter regularization. We develop and analyze a trust-region algorithm that solves a sequence of subproblems in which the regularization term and the binarity constraint are relaxed by a non-convex energy functional. We show how the parameter that controls the distinctiveness of the resulting phase field can be coupled to the trust-region radius updates and be driven to zero over the course of the iterations in order to obtain convergence to points that satisfy a first-order optimality condition of the limit problem under suitable regularity assumptions. Finally, we highlight and discuss the assumptions and restrictions of our approach and provide the first computational results for a motivating application in the field of control of acoustic waves in dissipative media.
Mathematics Subject Classification: 49M05 / 49M20 / 49Q15
Key words: Binary optimal control / perimeter regularization / phase-field approximation / trust-region methods / homotopy methods
© The authors. Published by EDP Sciences, SMAI 2025
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