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October  2017, 13(4): 1625-1640. doi: 10.3934/jimo.2017010

 School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

* Corresponding author: Jinyan Fan

Received  April 2016 Revised  October 2016 Published  December 2016

Fund Project: The authors are partially supported by NSFC 11171217 and 11571234

In this paper, we study subspace properties of the quadratically constrained quadratic program (QCQP). We prove that, if an appropriate subspace is chosen to satisfy subspace properties, then the solution of the QCQP lies in that subspace. So, we can solve the QCQP in that subspace rather than solve it in the original space. The computational cost could be reduced significantly if the dimension of the subspace is much smaller. We also show how to construct such subspaces and investigate their dimensions.

Citation: Xin Zhao, Jinyan Fan. On subspace properties of the quadratically constrained quadratic program. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1625-1640. doi: 10.3934/jimo.2017010
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