Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems

Abstract

This paper develops a condition for stability of the solution set of a system of nonlinear inequalities over a closed convex set in a Banach space, when the functions defining the inequalities are subjected to small perturbations. The condition involves the linearization of the system about a point; it is shown to be sufficient and, under a weak additional hypothesis, also necessary for stability. Quantitative estimates for the changes in the solution set are obtained.