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