SIAM Review
Enhancing RLT relaxations via a new class of semidefinite cuts
Journal of Global Optimization
A branch-and-cut algorithm for nonconvex quadratic programs with box constraints
Mathematical Programming: Series A and B
A New Verified Optimization Technique for the "Packing Circles in a Unit Square" Problems
SIAM Journal on Optimization
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations
Mathematical Programming: Series A and B
On the copositive representation of binary and continuous nonconvex quadratic programs
Mathematical Programming: Series A and B
Computable representations for convex hulls of low-dimensional quadratic forms
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
Optimization Methods & Software - GLOBAL OPTIMIZATION
Computational Optimization and Applications
Relaxing the optimality conditions of box QP
Computational Optimization and Applications
Journal of Global Optimization
Computational Optimization and Applications
Branch and cut algorithms for detecting critical nodes in undirected graphs
Computational Optimization and Applications
GloMIQO: Global mixed-integer quadratic optimizer
Journal of Global Optimization
Journal of Global Optimization
Valid constraints for the Point Packing in a Square problem
Discrete Applied Mathematics
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We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulation-linearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial portion of the feasible region corresponding to product terms in the RLT relaxation. On test problems we show that the use of SDP and RLT constraints together can produce bounds that are substantially better than either technique used alone. For highly symmetric problems we also consider the effect of symmetry-breaking based on tightened bounds on variables and/or order constraints.