Global convergence of $W^{1,\infty}$-steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space
Optimization and Control
2026-03-04 v1 Analysis of PDEs
Abstract
We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is realized in the Lipschitz topology. In addition, we prove a conditional convergence result for the resulting shapes in two space dimensions.
Keywords
Cite
@article{arxiv.2603.02812,
title = {Global convergence of $W^{1,\infty}$-steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space},
author = {Klaus Deckelnick and Philip J. Herbert and Michael Hinze},
journal= {arXiv preprint arXiv:2603.02812},
year = {2026}
}