On Infeasibility of Systems of Convex Analytic Inequalities

In this paper we address the problem of the infeasibility of systems defined by convex analytic 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 analyze properties of the irreducible sets, as well as infeasibility sets in connection with the set K, showing in particular 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 generalizations of a theory developed for the systems of quadratic and linear inequality constraints