Semismooth Newton Method for Boundary Bilinear Control
Optimization and Control
2024-03-06 v1
Abstract
We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state equation is performed and differentiability properties of the control-to-state mapping are shown. First and second order optimality conditions are derived. Our main result is the proof of superlinear convergence of the semismooth Newton method to local solutions satisfying no-gap second order sufficient optimality conditions as well as a strict complementarity condition.
Cite
@article{arxiv.2403.01135,
title = {Semismooth Newton Method for Boundary Bilinear Control},
author = {Eduardo Casas and Konstantinos Chrysafinos and Mariano Mateos},
journal= {arXiv preprint arXiv:2403.01135},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2309.07554