摘要
In a recent article,the authors provided an effective algorithm for both computing the global infimum of / and deciding whether or not the infimum of / is attained,where / is a multivariate polynomial over the field R of real numbers.As a complement,the authors investigate the semialgebraically connected components of minimum points of a polynomial function in this paper.For a given multivariate polynomial / over R,it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of / whenever /has its global minimum.
In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.
基金
supported by the National Natural Science Foundation of China under Grant No.11161034
the Science Foundation of the Education Department of Jiangxi Province under Grant No.Gjj12012
关键词
多项式函数
半代数
组件
连接
极值点
多元多项式
全局最小值
连通分量
Global minimum, minimum point, polynomial optimization, rational univariate represen-tation （RUR）, semi-algebraically connected component, strictly critical point.
