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. © Springer-Verlag 2006.