HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
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

Contributor : Elias Tsigaridas Connect in order to contact the contributor
Submitted on : Sunday, November 2, 2014 - 1:11:18 AM
Last modification on : Friday, January 21, 2022 - 3:21:21 AM
Long-term archiving on: : Tuesday, February 3, 2015 - 4:05:35 PM


Files produced by the author(s)


  • HAL Id : hal-00776280, version 2


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⟩



Record views


Files downloads