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We study linear programming relaxations of nonconvex quadratic programs givenby the reformulation-linearization technique (RLT), referred to as RLTrelaxations. We investigate the relations between the polyhedral properties ofthe feasible regions of a quadratic program and its RLT relaxation. Weestablish various connections between recession directions, boundedness, andvertices of the two feasible regions. Using these properties, we presentnecessary and sufficient exactness conditions for RLT relaxations. We then givea thorough discussion of how our results can be converted into simplealgorithmic procedures to construct instances of quadratic programs with exact,inexact, or unbounded RLT relaxations.

Polyhedral Properties of RLT Relaxations of Nonconvex Quadratic Programs and Their Implications on Exact Relaxations