On subspace properties of the quadratically constrained quadratic program

Xin Zhao; Jinyan Fan

doi:10.3934/jimo.2017010

Article Contents

2017, Volume 13, Issue 4: 1625-1640. Doi: 10.3934/jimo.2017010

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On subspace properties of the quadratically constrained quadratic program

Xin Zhao and
Jinyan Fan^,

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

* Corresponding author: Jinyan Fan
* Corresponding author: Jinyan Fan

Received: March 31, 2016

Revised: September 30, 2016

Published: November 2017

The authors are partially supported by NSFC 11171217 and 11571234.

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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.

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Mathematics Subject Classification: 49M30, 65K05, 90C20.

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References

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