On the stability of linear systems with an exact constraint set

Abstract

This paper deals with the stability of the intersection of a given set X ⊂ Rn with the solution, F ⊂ Rn, of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the solution set of the (possibly nonlinear) system formed by all the exact constraints (e.g., the sign constraints), a discrete subset of Rn (as Zn or {0, 1}n, as it happens in integer or Boolean programming) as well as the intersection of both kind of sets. Conditions are given for the intersection F ∩ X to remain nonempty (or empty) under sufficiently small perturbations of the data.