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Global minimization of multivariate polynomials using nonstandard methods

Authors :
Shuijing Xiao
Guangxing Zeng
Source :
Journal of Global Optimization. 53:391-415
Publication Year :
2011
Publisher :
Springer Science and Business Media LLC, 2011.

Abstract

The purpose of this paper is to present two algorithms for global minimization of multivariate polynomials. For a multivariate real polynomial f, we provide an effective algorithm for deciding whether or not the infimum of f is finite. In the case of f having a finite infimum, the infimum of f can be accurately coded as (h; a, b), where h is a real polynomial in one variable, a and b is two rational numbers with a < b, and (h, a, b) stands for the only real root of h in the open interval ]a, b[. Moreover, another algorithm is provided to decide whether or not the infimum of f is attained when the infimum of f is finite. Our methods are called “nonstandard”, because an infinitesimal element is introduced in our arguments.

Details

ISSN :
15732916 and 09255001
Volume :
53
Database :
OpenAIRE
Journal :
Journal of Global Optimization
Accession number :
edsair.doi...........4e17a06b193f87064d10cc8504bdced6
Full Text :
https://doi.org/10.1007/s10898-011-9718-x