Urysohn in action: separating semialgebraic sets by polynomials
Algebraic Geometry
2022-07-04 v1 Optimization and Control
Abstract
A classical result from topology called Uryshon's lemma asserts the existence of a continuous separator of two disjoint closed sets in a sufficiently regular topological space. In this work we make a search for this separator constructive and efficient in the context of real algebraic geometry. Namely, given two compact disjoint basic semialgebraic sets which are contained in an -dimensional box, we provide an algorithm that computes a separating polynomial greater than or equal to 1 on the first set and less than or equal to 0 on the second one.
Cite
@article{arxiv.2207.00570,
title = {Urysohn in action: separating semialgebraic sets by polynomials},
author = {Milan Korda and Jean-Bernard Lasserre and Alexey Lazarev and Victor Magron and Simone Naldi},
journal= {arXiv preprint arXiv:2207.00570},
year = {2022}
}
Comments
4 pages, 1 figure, submitted as en extended abstract for the last POEMA workshop