Polytopal balls arising in optimization
Metric Geometry
2022-04-14 v2 Combinatorics
Optimization and Control
Abstract
We study a family of polytopes and their duals, that appear in various optimization problems as the unit balls for certain norms. These two families interpolate between the hypercube, the unit ball for the -norm, and its dual cross-polytope, the unit ball for the -norm. We give combinatorial and geometric properties of both families of polytopes such as their -vector, their volume, and the volume of their boundary.
Cite
@article{arxiv.2011.05607,
title = {Polytopal balls arising in optimization},
author = {Antoine Deza and Jean-Baptiste Hiriart-Urruty and Lionel Pournin},
journal= {arXiv preprint arXiv:2011.05607},
year = {2022}
}
Comments
16 pages, 2 figures