L. Pournin

activity

20242026

collaborators

5 papers

math.OC2026

Geometry of Sparsity-Inducing Norms

Jean-Philippe Chancelier, Michel de Lara, Antoine Deza +1

Sparse optimization seeks an optimal solution with few nonzero entries. To achieve this, it is common to add to the criterion a penalty term proportional to the $ℓ_{1}$ -norm, whic…

math.MG2026

Flat simplices and kissing polytopes

Antoine Deza, Lionel Pournin

We consider how flat a lattice simplex contained in the hypercube $[0, k]^{d}$ can be. This question is related to the notion of kissing polytopes: two lattice polytopes contained in…

math.MG2025

Deep sections of the hypercube

Lionel Pournin

Consider a non-negative number $t$ and a hyperplane $H$ of $R^{d}$ whose distance to the center of the hypercube $[0, 1]^{d}$ is $t$ . If $t$ is equal to $0$ and $H$ is orthogon…

math.MG2025

Kissing polytopes in dimension 3

Antoine Deza, Zhongyuan Liu, Lionel Pournin

It is shown that the smallest possible distance between two disjoint lattice polytopes contained in the cube $[0, k]^{3}$ is exactly $\frac{1}{2 ( 2 k ^{2} - 4 k + 5 ) ( 2 k ^{2} - 2 k + 1 )}$ for…

math.CO2024

Small kissing polytopes

Antoine Deza, Zhongyuan Liu, Lionel Pournin

A lattice $(d, k)$ -polytope is the convex hull of a set of points in $R^{d}$ whose coordinates are integers ranging between $0$ and $k$ . We consider the smallest possible dis…