Parametric Shape Optimization using the Support Function
Optimization and Control
2021-11-01 v3
Abstract
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization problems under various constraints. We propose a numerical framework in dimensions two and three and we present applications from the field of convex geometry. We consider the optimization of functionals depending on the volume, perimeter and Dirichlet Laplace eigenvalues under the aforementioned constraints. In particular we confirm numerically Meissner's conjecture, regarding three dimensional bodies of constant width with minimal volume.
Cite
@article{arxiv.1809.00254,
title = {Parametric Shape Optimization using the Support Function},
author = {Pedro R. S. Antunes and Beniamin Bogosel},
journal= {arXiv preprint arXiv:1809.00254},
year = {2021}
}