Ellipsoidal mixed-integer representability

Representability results for mixed-integer linear systems play a fundamental role in optimization since they give geometric characterizations of the feasible sets that can be formulated by mixed-integer linear programming. We consider a natural extension of mixed-integer linear systems obtained by adding just one ellipsoidal inequality. The set of points that can be described, possibly using additional variables, by these systems are called ellipsoidal mixed-integer representable. In this work, we give geometric conditions that characterize ellipsoidal mixed-integer representable sets.