On the minimum of a positive polynomial over the standard simplex

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, Gabriela Tali, Perrucci, Daniel
Publicado: 2010
Materias:
Optimization on polyhedra
Positivity of polynomials
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v45_n4_p434_Jeronimo
http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_07477171_v45_n4_p434_Jeronimo
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spelling paper:paper_07477171_v45_n4_p434_Jeronimo2023-06-08T15:45:10Z On the minimum of a positive polynomial over the standard simplex Jeronimo, Gabriela Tali Perrucci, Daniel 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v45_n4_p434_Jeronimo 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)
topic Optimization on polyhedra
Positivity of polynomials
spellingShingle Optimization on polyhedra
Positivity of polynomials
Jeronimo, Gabriela Tali
Perrucci, Daniel
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.
author Jeronimo, Gabriela Tali
Perrucci, Daniel
author_facet Jeronimo, Gabriela Tali
Perrucci, Daniel
author_sort Jeronimo, Gabriela Tali
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v45_n4_p434_Jeronimo
http://hdl.handle.net/20.500.12110/paper_07477171_v45_n4_p434_Jeronimo
work_keys_str_mv AT jeronimogabrielatali ontheminimumofapositivepolynomialoverthestandardsimplex
AT perruccidaniel ontheminimumofapositivepolynomialoverthestandardsimplex
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