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

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 nonco...

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Autores principales:	Jeronimo, Gabriela Tali, Perrucci, Daniel
Publicado:	2013
Materias:	Polynomial optimization Separation bounds Absolute values Algebraic degrees Connected component Lower bounds Polynomial functions Semi-algebraic set Semi-algebraic sets Functions Separation Set theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10526234_v23_n1_p241_Jeronimo http://hdl.handle.net/20.500.12110/paper_10526234_v23_n1_p241_Jeronimo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_10526234_v23_n1_p241_Jeronimo
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spelling	paper:paper_10526234_v23_n1_p241_Jeronimo2025-07-30T18:38:53Z On the minimum of a polynomial function on a basic closed semialgebraic set and applications Jeronimo, Gabriela Tali Perrucci, Daniel Polynomial optimization Separation bounds Absolute values Algebraic degrees Connected component Lower bounds Polynomial functions Polynomial optimization Semi-algebraic set Semi-algebraic sets Functions Separation Set theory 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 noncompact 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. © 2013 Society for Industrial and Applied Mathematics. Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Perrucci, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10526234_v23_n1_p241_Jeronimo http://hdl.handle.net/20.500.12110/paper_10526234_v23_n1_p241_Jeronimo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Polynomial optimization Separation bounds Absolute values Algebraic degrees Connected component Lower bounds Polynomial functions Polynomial optimization Semi-algebraic set Semi-algebraic sets Functions Separation Set theory
spellingShingle	Polynomial optimization Separation bounds Absolute values Algebraic degrees Connected component Lower bounds Polynomial functions Polynomial optimization Semi-algebraic set Semi-algebraic sets Functions Separation Set theory Jeronimo, Gabriela Tali Perrucci, Daniel On the minimum of a polynomial function on a basic closed semialgebraic set and applications
topic_facet	Polynomial optimization Separation bounds Absolute values Algebraic degrees Connected component Lower bounds Polynomial functions Polynomial optimization Semi-algebraic set Semi-algebraic sets Functions Separation Set theory
description	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 noncompact 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. © 2013 Society for Industrial and Applied Mathematics.
author	Jeronimo, Gabriela Tali Perrucci, Daniel
author_facet	Jeronimo, Gabriela Tali Perrucci, Daniel
author_sort	Jeronimo, Gabriela Tali
title	On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_short	On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_full	On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_fullStr	On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_full_unstemmed	On the minimum of a polynomial function on a basic closed semialgebraic set and applications
title_sort	on the minimum of a polynomial function on a basic closed semialgebraic set and applications
publishDate	2013
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10526234_v23_n1_p241_Jeronimo http://hdl.handle.net/20.500.12110/paper_10526234_v23_n1_p241_Jeronimo
work_keys_str_mv	AT jeronimogabrielatali ontheminimumofapolynomialfunctiononabasicclosedsemialgebraicsetandapplications AT perruccidaniel ontheminimumofapolynomialfunctiononabasicclosedsemialgebraicsetandapplications
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On the minimum of a polynomial function on a basic closed semialgebraic set and applications

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