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Improved approximation results on standard quartic polynomial optimization

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Abstract

In this paper, we consider the problem of approximately solving standard quartic polynomial optimization (SQPO). Using its reformulation as a copositive tensor programming, we show how to approximate the optimal solution of SQPO by using a series of polyhedral cones to approximate the cone of copositive tensors. The established quality of approximation is sharper than the ones studied in the literature. As an interesting extension, we also propose some approximation bounds on multi-homogenous polynomial optimization problems.

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Acknowledgements

The authors would like to thank the two anonymous referees for their comments helping us improve the presentation of the paper. The first two authors were supported in part by NSFC at Grant Nos. (11171083, 11301123, 11571087) and Zhejiang Provincial NSF at Grant Nos. (LZ14A01003, LY17A010028). The third author was supported by the Hong Kong Research Grant Council (Grant Nos. PolyU 502510, 502111, 501212 and 501913).

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Chen Ling & Hongjin He

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liqun Qi

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  1. Chen Ling
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  2. Hongjin He
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  3. Liqun Qi
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Correspondence to Hongjin He.

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Ling, C., He, H. & Qi, L. Improved approximation results on standard quartic polynomial optimization. Optim Lett 11, 1767–1782 (2017). https://doi.org/10.1007/s11590-016-1094-5

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  • DOI: https://doi.org/10.1007/s11590-016-1094-5

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