Global minimization of a multivariate polynomial using matrix methods

被引：49

作者：

Hanzon, B

Jibetean, D

机构：

[1] Free Univ Amsterdam, NL-1081 HV Amsterdam, Netherlands

[2] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2003年 / 27卷 / 01期

关键词：

algebraic functions; connected components; eigenvalue problems; global minimum; infimum; Grobner bases; polynomial matrices; polynomial optimization;

D O I：

10.1023/A:1024664432540

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 [运筹学与控制论]; 12 [管理学]; 1201 [管理科学与工程]; 1202 [工商管理学]; 120202 [企业管理];

摘要：

The problem of minimizing a polynomial function in several variables over R-n is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimal value and finds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a minimum the algorithm computes its infimum. No assumption is made on the polynomial.

引用

页码：1 / 23

页数：23

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