Representability results play a fundamental role in optimization since they provide characterizations of the feasible sets that arise from optimization problems. In this paper we study the sets that appear in the feasibility version of mixed binary convex quadratic optimization problems. We provide a complete characterization of the sets that can be obtained as the projection of such feasible regions. In order to obtain this result, we first provide a complete characterization of these sets in the special cases where (i) the feasible region is bounded, (ii) only binary extended variables are present, and (iii) only continuous variables are present.
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