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Structured linear reformulation of binary quadratically constrained quadratic programs

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Abstract

This paper presents a new linear reformulation to convert a binary quadratically constrained quadratic program into a 0–1 mixed integer linear program. By exploiting the symmetric structure of the quadratic terms embedded in the objective and constraint functions, the proposed linear reformulation requires fewer variables and constraints than other known O(n)-sized linear reformulations. Theoretical proof shows the proposed reformulation provides a tighter linearization for each quadratic term comparing to other known linear reformulations. Extensive numerical experiments support the superior computational efficiency of the proposed reformulation in terms of the running time and number of nodes explored.

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Acknowledgements

This work has been sponsored by US Army Research Office Grant #W911NF-15-1-0223.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA

    Shan Jiang, Shu-Cherng Fang & Qi An

  2. Department of Systems Engineering and Engineering Management, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Tiantian Nie

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  1. Shan Jiang
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  2. Shu-Cherng Fang
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  3. Tiantian Nie
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  4. Qi An
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Correspondence to Tiantian Nie.

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Jiang, S., Fang, SC., Nie, T. et al. Structured linear reformulation of binary quadratically constrained quadratic programs. Optim Lett 14, 611–636 (2020). https://doi.org/10.1007/s11590-018-1361-8

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