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Cutting planes for RLT relaxations of mixed 0–1 polynomial programs

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Abstract

The reformulation–linearization technique, due to Sherali and Adams, can be used to construct hierarchies of linear programming relaxations of mixed 0–1 polynomial programs. As one moves up the hierarchy, the relaxations grow stronger, but the number of variables increases exponentially. We present a procedure that generates cutting planes at any given level of the hierarchy, by optimally weakening linear inequalities that are valid at any given higher level. Computational experiments, conducted on instances of the quadratic knapsack problem, indicate that the cutting planes can close a significant proportion of the integrality gap.

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Acknowledgments

We are grateful to the late Alberto Caprara for giving us his QKP code. Thanks are also due to two anonymous referees for several helpful comments and suggestions.

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  1. Department of Management Science, Lancaster University Management School, Lancaster, LA1 4YX, UK

    Franklin Djeumou Fomeni, Konstantinos Kaparis & Adam N. Letchford

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  1. Franklin Djeumou Fomeni
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  2. Konstantinos Kaparis
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  3. Adam N. Letchford
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Correspondence to Adam N. Letchford.

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Fomeni, F.D., Kaparis, K. & Letchford, A.N. Cutting planes for RLT relaxations of mixed 0–1 polynomial programs. Math. Program. 151, 639–658 (2015). https://doi.org/10.1007/s10107-015-0863-8

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  • DOI: https://doi.org/10.1007/s10107-015-0863-8

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