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Semidefinite approximation bound for a class of nonhomogeneous nonconvex quadratically constrained quadratic programming problem

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Abstract

In this paper, we consider a class of nonconvex nonhomogeneous quadratically constrained quadratic optimization problem. We derive some sufficient condition for the input data, and then establish a semi-definite approximation bound based on a randomization algorithm. The approximation bound is optimal in the order of m in general under the given restriction on the input data.

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Notes

  1. There are some existing ways to generate a normally distributed random vector. If necessary, we can resort to the help of some software, e.g., the “mvnrnd” function in MATLAB software.

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Acknowledgements

This research was supported by National Natural Science Foundation of China under Grants 11571221.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Zi Xu, Siqi Tao & Kaiyao Lou

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  1. Zi Xu
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  2. Siqi Tao
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  3. Kaiyao Lou
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Correspondence to Zi Xu.

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Xu, Z., Tao, S. & Lou, K. Semidefinite approximation bound for a class of nonhomogeneous nonconvex quadratically constrained quadratic programming problem. Optim Lett 13, 837–845 (2019). https://doi.org/10.1007/s11590-018-1283-5

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  • DOI: https://doi.org/10.1007/s11590-018-1283-5

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