ERROR BOUNDS FOR SOME SEMIDEFINITE PROGRAMMING APPROACHES TO POLYNOMIAL MINIMIZATION ON THE HYPERCUBE

被引：36
|
作者：
de Klerk, Etienne [1 ]
Laurent, Monique [1 ,2 ]
机构：
[1] Tilburg Univ, Dept Econometr & Operat Res, NL-5000 LE Tilburg, Netherlands
[2] Ctr Wiskunde & Informat, NL-1098 XG Amsterdam, Netherlands
来源：
SIAM JOURNAL ON OPTIMIZATION | 2010年 / 20卷 / 06期
关键词：
Positivstellensatz; positive polynomial; sum of squares of polynomials; bound constrained optimization of polynomials; multivariate Bernstein approximation; semidefinite programming; SEMI-ALGEBRAIC SETS; OPTIMIZATION; COMPLEXITY; POSITIVSTELLENSATZ; MOMENTS; SIMPLEX; THEOREM; SQUARES;
D O I：
10.1137/100790835
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the problem of minimizing a polynomial on the hypercube [0, 1](n) and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmudgen [Math. Ann., 289 (1991), pp. 203-206]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the hypercube.
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页码：3104 / 3120
页数：17
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