Convex quadratic relaxations of nonconvex quadratically constrained quadratic programs

Nonconvex quadratic constraints can be linearized to obtain relaxations in a well-understood manner. We propose to tighten the relaxation by using second-order cone constraints, resulting in a convex quadratic relaxation. Our quadratic approximation to the bilinear term is compared to the linear McCormick bounds. The second-order cone constraints are based on linear combinations of pairs of variables. With good bounds on these linear combinations, the resulting constraints strengthen the McCormick bounds. Computational results are given, which indicate that the convex quadratic relaxation can dramatically improve the solution times for some problems.

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