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Journal of Systems Science and Complexity

, Volume 26, Issue 6, pp 1028–1046 | Cite as

Semi-algebraically connected components of minimum points of a polynomial function

  • Shuijing XiaoEmail author
  • Guangxing Zeng
Article
  • 54 Downloads

Abstract

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.

Key words

Global minimum minimum point polynomial optimization rational univariate representation (RUR) semi-algebraically connected component strictly critical point 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsNanchang UniversityNanchangChina

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