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Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints

Author

Listed:
  • Sven de Vries

    (Trier University)

  • Bernd Perscheid

    (Trier University)

Abstract

Cutting planes from the Boolean Quadric Polytope can be used to reduce the optimality gap of the $$\mathcal {NP}$$ NP -hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal–Gomory closure of the Boolean Quadric Polytope are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which allows to optimize over the Chvátal–Gomory closure without repeated calls to separation algorithms and has less inequalities than the formulation provided by Boros et al. (SIAM J Discrete Math 5(2):163–177, 1992) for sparse matrices. In a computational study, we confirm the strength of this relaxation and show that we can provide very strong bounds for the BoxQP, even with a plain linear program. The resulting bounds are significantly stronger than these from Bonami et al. (Math Program Comput 10(3):333–382, 2018), which arise from separating A-odd cycle inequalities heuristically.

Suggested Citation

  • Sven de Vries & Bernd Perscheid, 2022. "Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints," Journal of Global Optimization, Springer, vol. 84(3), pages 591-606, November.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:3:d:10.1007_s10898-022-01157-9
    DOI: 10.1007/s10898-022-01157-9
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    References listed on IDEAS

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    1. Samuel Burer & Dieter Vandenbussche, 2009. "Globally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound," Computational Optimization and Applications, Springer, vol. 43(2), pages 181-195, June.
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