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Journal of Global Optimization

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

Sven de Vries, Bernd Perscheid

Published May 9, 2022• 1 citation
Publisher

Abstract

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 allA-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.

DOI
10.1007/s10898-022-01157-9

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