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Quadratic programs with box constraints involve minimizing a possiblynonconvex quadratic function subject to lower and upper bounds on eachvariable. This is a well-known NP-hard problem that frequently arises invarious applications. We focus on two convex relaxations, namely the RLT(Reformulation-Linearization Technique) relaxation and the SDP-RLT relaxationobtained by adding semidefinite constraints to the RLT relaxation. Bothrelaxations yield lower bounds on the optimal value of a quadratic program withbox constraints. We present complete algebraic descriptions of the set ofinstances that admit exact RLT relaxations as well as those that admit exactSDP-RLT relaxations. We show that our descriptions can be converted intoalgorithms for efficiently constructing instances with exact or inexactrelaxations.

On Exact and Inexact RLT and SDP-RLT Relaxations of Quadratic Programs with Box Constraints