We study linear programming relaxations of nonconvex quadratic programs given
by the reformulation-linearization technique (RLT), referred to as RLT
relaxations. We investigate the relations between the polyhedral properties of
the feasible regions of a quadratic program and its RLT relaxation. We
establish various connections between recession directions, boundedness, and
vertices of the two feasible regions. Using these properties, we present
necessary and sufficient exactness conditions for RLT relaxations. We then give
a thorough discussion of how our results can be converted into simple
algorithmic procedures to construct instances of quadratic programs with exact,
inexact, or unbounded RLT relaxations.Comment: Technical Report, School of Mathematics, The University of Edinburgh,
Edinburgh, EH9 3FD, Scotland, United Kingdo