Frontiers of Mathematics in China

, Volume 12, Issue 6, pp 1409–1426 | Cite as

Approximation algorithms for nonnegative polynomial optimization problems over unit spheres

  • Xinzhen Zhang
  • Guanglu Zhou
  • Louis Caccetta
  • Mohammed Alqahtani
Research Article
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Abstract

We consider approximation algorithms for nonnegative polynomial optimization problems over unit spheres. These optimization problems have wide applications e.g., in signal and image processing, high order statistics, and computer vision. Since these problems are NP-hard, we are interested in studying on approximation algorithms. In particular, we propose some polynomial-time approximation algorithms with new approximation bounds. In addition, based on these approximation algorithms, some efficient algorithms are presented and numerical results are reported to show the efficiency of our proposed algorithms.

Keywords

Approximation algorithm polynomial optimization approximation bound 

MSC

65K10 90C25 90C30 
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Notes

Acknowledgements

The authors would like to thank the reviewers for their insightful comments which help to improve the presentation of the paper. The first author’s work was supported by the National Natural Science Foundation of China (Grant No. 11471242) and the work of the second author was supported by the National Natural Science Foundation of China (Grant No. 11601261).

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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Xinzhen Zhang
    • 1
  • Guanglu Zhou
    • 2
  • Louis Caccetta
    • 2
  • Mohammed Alqahtani
    • 2
  1. 1.School of MathematicsTianjin UniversityTianjinChina
  2. 2.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia

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