# Numerical approximation of optimal convex shapes

arXiv: https://arxiv.org/abs/1810.10735 · HTML: https://mlsanity.com/paper/1810.10735/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2018.

## Built on by (most cited first, 2 of 2)

- [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)

This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem. Moreover, we prove the convergence of discretizations in two-dimensional situations. A numerical algorithm is devised that iteratively solves the discrete formulation. Numerical experiments show that optimal convex shapes are generally non-smooth and that three-dimensional problems require an appropriate relaxation of the convexity condition.