On the minimum of a polynomial function on a basic closed semialgebraic set and applications
Algebraic Geometry
2011-12-05 v1 Computational Geometry
Abstract
We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.
Cite
@article{arxiv.1112.0544,
title = {On the minimum of a polynomial function on a basic closed semialgebraic set and applications},
author = {Gabriela Jeronimo and Daniel Perrucci and Elias Tsigaridas},
journal= {arXiv preprint arXiv:1112.0544},
year = {2011}
}