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Abstract:

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.

Registro:

Documento: Artículo
Título:On the minimum of a positive polynomial over the standard simplex
Autor:Jeronimo, G.; Perrucci, D.
Filiación:Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:Optimization on polyhedra; Positivity of polynomials
Año:2010
Volumen:45
Número:4
Página de inicio:434
Página de fin:442
DOI: http://dx.doi.org/10.1016/j.jsc.2010.01.001
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v45_n4_p434_Jeronimo.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v45_n4_p434_Jeronimo

Referencias:

  • Basu, S., Leroy, R., Roy, M.-F., 2009. A bound on the minimum of a real positive polynomial over the standard simplex, Manuscript. Available at: arXiv:0902.3304; Basu, S., Pollack, R., Roy, M.-F., (2006) Algorithms and Computation in Mathematics, 10. , Springer-Verlag, Berlin
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Citas:

---------- APA ----------
Jeronimo, G. & Perrucci, D. (2010) . On the minimum of a positive polynomial over the standard simplex. Journal of Symbolic Computation, 45(4), 434-442.
http://dx.doi.org/10.1016/j.jsc.2010.01.001
---------- CHICAGO ----------
Jeronimo, G., Perrucci, D. "On the minimum of a positive polynomial over the standard simplex" . Journal of Symbolic Computation 45, no. 4 (2010) : 434-442.
http://dx.doi.org/10.1016/j.jsc.2010.01.001
---------- MLA ----------
Jeronimo, G., Perrucci, D. "On the minimum of a positive polynomial over the standard simplex" . Journal of Symbolic Computation, vol. 45, no. 4, 2010, pp. 434-442.
http://dx.doi.org/10.1016/j.jsc.2010.01.001
---------- VANCOUVER ----------
Jeronimo, G., Perrucci, D. On the minimum of a positive polynomial over the standard simplex. J. Symb. Comput. 2010;45(4):434-442.
http://dx.doi.org/10.1016/j.jsc.2010.01.001