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Approximation algorithms for nonnegative polynomial optimization problems over unit spheres

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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.

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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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Authors and Affiliations

  1. School of Mathematics, Tianjin University, Tianjin, 300072, China

    Xinzhen Zhang

  2. Department of Mathematics and Statistics, Curtin University, Perth, Australia

    Guanglu Zhou, Louis Caccetta & Mohammed Alqahtani

Authors
  1. Xinzhen Zhang
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  2. Guanglu Zhou
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  3. Louis Caccetta
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  4. Mohammed Alqahtani
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Correspondence to Guanglu Zhou.

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Zhang, X., Zhou, G., Caccetta, L. et al. Approximation algorithms for nonnegative polynomial optimization problems over unit spheres. Front. Math. China 12, 1409–1426 (2017). https://doi.org/10.1007/s11464-017-0644-1

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  • DOI: https://doi.org/10.1007/s11464-017-0644-1

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