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Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints

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Abstract

This paper studies the relationship between the so-called bi-quadratic optimization problem and its semidefinite programming (SDP) relaxation. It is shown that each r-bound approximation solution of the relaxed bi-linear SDP can be used to generate in randomized polynomial time an \({\mathcal{O}(r)}\)-approximation solution of the original bi-quadratic optimization problem, where the constant in \({\mathcal{O}(r)}\) does not involve the dimension of variables and the data of problems. For special cases of maximization model, we provide an approximation algorithm for the considered problems.

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Author notes

  1. Chen Ling

    Present address: School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, China

Authors and Affiliations

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

    Xinzhen Zhang & Liqun Qi

  2. School of Science, Hangzhou Dianzi University, 310018, Hangzhou, China

    Chen Ling

Authors
  1. Xinzhen Zhang
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  2. Chen Ling
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  3. Liqun Qi
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Corresponding author

Correspondence to Chen Ling.

Additional information

Xinzhen Zhang work is supported by the National Natural Science Foundation of China (10771120).

Chen Ling work is supported by Chinese NSF Grants 10871168 and 10971187, and a Hong Kong Polytechnic University Postdoctoral Fellowship.

Liqun Qi work is supported by the Hong Kong Research Grant Council.

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Zhang, X., Ling, C. & Qi, L. Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints. J Glob Optim 49, 293–311 (2011). https://doi.org/10.1007/s10898-010-9545-5

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