Skip to Main content Skip to Navigation
Journal articles

On the minimum of a polynomial function on a basic closed semialgebraic set and applications

Gabriella Jeronimo 1 Daniel Perrucci 1 Elias Tsigaridas 2
2 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
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. We also present extensions of these results to non-compact situations. 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download

https://hal.inria.fr/hal-00776280
Contributor : Elias Tsigaridas <>
Submitted on : Sunday, November 2, 2014 - 1:11:18 AM
Last modification on : Friday, January 8, 2021 - 5:42:02 PM
Long-term archiving on: : Tuesday, February 3, 2015 - 4:05:35 PM

File

MinDistance_revised.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00776280, version 2

Citation

Gabriella Jeronimo, Daniel Perrucci, Elias Tsigaridas. On the minimum of a polynomial function on a basic closed semialgebraic set and applications. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2013, 23 (1), pp.241--255. ⟨hal-00776280v2⟩

Share

Metrics

Record views

395

Files downloads

1192