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Alternating direction method for bi-quadratic programming

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Abstract

Bi-quadratic programming (Bi-QP for short) was studied systematically in Ling et al. (SIAM J. Optim. 20:1286–1320, 2009) due to its various applications in engineering as well as optimization. Several approximation methods were given in the same paper since it is NP-hard. In this paper, we introduce a quadratic SDP relaxation of Bi-QP and discuss the approximation ratio of the method. In particular, by exploiting the favorite structure of the quadratic SDP relaxation, we propose an alternating direction method for solving such a problem and show that the method is globally convergent without any assumption. Some preliminary numerical results are reported which show the effectiveness of the method proposed in this paper.

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Author notes

  1. Sheng-Long Hu

    Present address: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China

Authors and Affiliations

  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, People’s Republic of China

    Sheng-Long Hu & Zheng-Hai Huang

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  1. Sheng-Long Hu
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Correspondence to Zheng-Hai Huang.

Additional information

This work is partially supported by the National Natural Science Foundation of China (Grant No. 10871144).

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Hu, SL., Huang, ZH. Alternating direction method for bi-quadratic programming. J Glob Optim 51, 429–446 (2011). https://doi.org/10.1007/s10898-010-9635-4

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  • DOI: https://doi.org/10.1007/s10898-010-9635-4

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