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A compact variant of the QCR method for quadratically constrained quadratic 0–1 programs

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Abstract

Quadratic Convex Reformulation (QCR) is a technique that was originally proposed for quadratic 0–1 programs, and then extended to various other problems. It is used to convert non-convex instances into convex ones, in such a way that the bound obtained by solving the continuous relaxation of the reformulated instance is as strong as possible. In this paper, we focus on the case of quadratically constrained quadratic 0–1 programs. The variant of QCR previously proposed for this case involves the addition of a quadratic number of auxiliary continuous variables. We show that, in fact, at most one additional variable is needed. Some computational results are also presented.

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Acknowledgments

The second author was partially supported by the Engineering and Physical Sciences Research Council under grant EP/D072662/1.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127 , Pisa, Italy

    Laura Galli

  2. Department of Management Science, Lancaster University, Lancaster, LA1 4YW, UK

    Adam N. Letchford

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  1. Laura Galli
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  2. Adam N. Letchford
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Correspondence to Adam N. Letchford.

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Galli, L., Letchford, A.N. A compact variant of the QCR method for quadratically constrained quadratic 0–1 programs. Optim Lett 8, 1213–1224 (2014). https://doi.org/10.1007/s11590-013-0676-8

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  • DOI: https://doi.org/10.1007/s11590-013-0676-8

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