Global minimization of multivariate polynomials using nonstandard methods |
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Authors: | Guangxing Zeng Shuijing Xiao |
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Institution: | 1. Department of Mathematics, Nanchang University, 330031, Nanchang, China
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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. |
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