A note on Burer's copositive representation of mixed-binary QPs

In an important paper, Burer (2009) recently showed how to reformulate general mixed-binary quadratic optimization problems (QPs) into copositive programs where a linear functional is minimized over a linearly constrained subset of the cone of completely positive matrices. In this note we interpret the implication from a topological point of view, showing that the Minkowski sum of the lifted feasible set and the lifted recession cone gives exactly the closure of the former. We also discuss why feasibility of the copositive program implies feasibility of the original mixed-binary QP, which can be derived from the arguments in Burer without any further condition.