Shape optimisation with nonsmooth cost functions: from theory to numerics
Optimization and Control
2016-04-05 v2
Abstract
This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-derivative of the cost function by employing the averaged adjoint approach and maximal elliptic regularity. Furthermore we characterise stationary points and show how to compute steepest descent direc- tions theoretically and practically. Finally, we present some numerical results for a simple toy problem and compare them with the smooth case. We also compare the convergence rates and obtain higher rates in the nonsmooth case.
Cite
@article{arxiv.1603.08235,
title = {Shape optimisation with nonsmooth cost functions: from theory to numerics},
author = {Kevin Sturm},
journal= {arXiv preprint arXiv:1603.08235},
year = {2016}
}