We
derive and study a reformulation technique for general 0–1
quadratic programs (QP) that uses diagonal as well as nondiagonal
perturbation of the objective function. The technique is an extension
of the Quadratic Convex Reformulation (QCR) method developed by Billionnet
and co-workers, adding nondiagonal perturbations, whereas QCR is in
a sense diagonal. In this work a set of redundant reformulation-linearization
technique (RLT) inequalities are included in the problem. The redundant
inequalities are used to induce nondiagonal perturbations of the objective
function that improve the bounding characteristics of the continuous
relaxation. The optimal convexification is obtained from the solution
of a semidefinite program. We apply the nondiagonal QCR (NDQCR) technique
to four different types of problems and compare the bounding properties
and solution times with the original QCR method. The proposed method
outperforms the original QCR method on all four types of test problems.
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