# Parametric Shape Optimization using the Support Function

arXiv: https://arxiv.org/abs/1809.00254 · HTML: https://mlsanity.com/paper/1809.00254/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2018.

## Built on by (most cited first, 3 of 3)

- [A Binary Characterization Method for Shape Convexity and Applications](https://mlsanity.com/paper/2203.11395/) (2022)
- [Numerical exploration of the range of shape functionals using neural networks](https://mlsanity.com/paper/2602.14881/) (2026)
- [Parametrizing Convex Sets Using Sublinear Neural Networks](https://mlsanity.com/paper/2605.03520/) (2026)

## Abstract (arXiv)

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.