Efficient Techniques for Shape Optimization with Variational Inequalities using Adjoints
Optimization and Control
2020-12-17 v4
Abstract
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational inequalities of the first kind, so-called obstacle-type problems. Under appropriate assumptions, we prove existence of adjoints for regularized problems and convergence to limiting objects of the unregularized problem. Moreover, we derive existence and closed form of shape derivatives for the regularized problem and prove convergence to a limit object. Based on this analysis, an efficient optimization algorithm is devised and tested numerically.
Cite
@article{arxiv.1904.08650,
title = {Efficient Techniques for Shape Optimization with Variational Inequalities using Adjoints},
author = {Daniel Luft and Volker H. Schulz and Kathrin Welker},
journal= {arXiv preprint arXiv:1904.08650},
year = {2020}
}