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
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v45_n4_p434_Jeronimo_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

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spelling	I28-R145-paper_07477171_v45_n4_p434_Jeronimo_oai2024-08-16 Jeronimo, G. Perrucci, D. 2010 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. application/pdf http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Symb. Comput. 2010;45(4):434-442 Optimization on polyhedra Positivity of polynomials On the minimum of a positive polynomial over the standard simplex info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v45_n4_p434_Jeronimo_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v45_n4_p434_Jeronimo_oai
work_keys_str_mv	AT jeronimog ontheminimumofapositivepolynomialoverthestandardsimplex AT perruccid ontheminimumofapositivepolynomialoverthestandardsimplex
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On the minimum of a positive polynomial over the standard simplex

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