On the minimum of a positive polynomial over the standard simplex

被引：13

作者：

Jeronimo, Gabriela ^{[1
,2
]}

Perrucci, Daniel ^{[1
]}

机构：

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, RA-1033 Buenos Aires, DF, Argentina

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2010年 / 45卷 / 04期

关键词：

Positivity of polynomials; Optimization on polyhedra; POLYAS THEOREM;

D O I：

10.1016/j.jsc.2010.01.001

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize tau of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：434 / 442

页数：9

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