On the minimum of a positive polynomial over the standard simplex

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We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coeffi...

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Autores principales: Jeronimo, G., Perrucci, D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
Materias:
Optimization on polyhedra
Positivity of polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_07477171_v45_n4_p434_Jeronimo2023-06-12T16:48:14Z On the minimum of a positive polynomial over the standard simplex J. Symb. Comput. 2010;45(4):434-442 Jeronimo, G. Perrucci, D. Optimization on polyhedra Positivity of polynomials We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex. © 2010 Elsevier Ltd. All rights reserved. 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. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Optimization on polyhedra
Positivity of polynomials
spellingShingle Optimization on polyhedra
Positivity of polynomials
Jeronimo, G.
Perrucci, D.
On the minimum of a positive polynomial over the standard simplex
topic_facet Optimization on polyhedra
Positivity of polynomials
description We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of Rk, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex. © 2010 Elsevier Ltd. All rights reserved.
format Artículo
Artículo
publishedVersion
author Jeronimo, G.
Perrucci, D.
author_facet Jeronimo, G.
Perrucci, D.
author_sort Jeronimo, G.
title On the minimum of a positive polynomial over the standard simplex
title_short On the minimum of a positive polynomial over the standard simplex
title_full On the minimum of a positive polynomial over the standard simplex
title_fullStr On the minimum of a positive polynomial over the standard simplex
title_full_unstemmed On the minimum of a positive polynomial over the standard simplex
title_sort on the minimum of a positive polynomial over the standard simplex
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo
work_keys_str_mv AT jeronimog ontheminimumofapositivepolynomialoverthestandardsimplex
AT perruccid ontheminimumofapositivepolynomialoverthestandardsimplex
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