We present semidefinite relaxations of nonconvex, box-constrained quadratic programming, which incorporate the first- and second-order necessary optimality conditions. We compare these relaxations with a basic semidefinite relaxation due to Shor, particularly in the context of branch-and-bound to determine a global optimal solution, where it is shown empirically that the new relaxations are significantly stronger. We also establish theoretical relationships between the new relaxations and Shor’s relaxation.
Citation
Manuscript, Department of Management Sciences, University of Iowa, Iowa City, IA 52240, USA, October 2007.