Infeasibility analysis for systems of quadratic convex inequalities

In this paper we address the problem of the infeasibility of systems defined by quadratic convex inequality constraints. In particular, we investigate properties of irreducible infeasible sets and provide an algorithm that identifies a set of all constraints (K) that may affect the feasibility status of the system after some perturbation of the right-hand sides. We show that all irreducible sets, as well as infeasibility sets, are subsets of the set K, and that every infeasible system contains an inconsistent subsystem of cardinality not greater than the number of variables plus one. The results presented in this paper are also applicable to linear systems.