# On improving convex quadratic programming relaxation for the quadratic assignment problem

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## Abstract

Relaxation techniques play a great role in solving the quadratic assignment problem, among which the convex quadratic programming bound (QPB) is competitive with existing bounds in the trade-off between cost and quality. In this article, we propose two new lower bounds based on QPB. The first dominates QPB at a high computational cost, which is shown equivalent to the recent second-order cone programming bound. The second is strictly tighter than QPB in most cases, while it is solved as easily as QPB.

## Keywords

Quadratic assignment problem Lower bound Capacitated transportation problem Quadratic programming## Mathematics Subject Classification

90C10 90C20 90C26## Notes

### Acknowledgments

The authors are grateful to the two anonymous referees for their valuable comments and suggestions that have greatly helped the authors improve the paper. This research was supported by National Natural Science Foundation of China under grants 11001006 and 91130019/A011702, by the fund of State Key Laboratory of Software Development Environment under grant SKLSDE-2013ZX-13.

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