Stability of error bounds for conic subsmooth inequalities

Abstract

Under either linearity or convexity assumption, several authors have studied the stability of error bounds for inequality systems when the concerned data undergo small perturbations. In this paper, we consider the corresponding issue for a more general conic inequality (most of the constraint systems in optimization can be described by an inequality of this type). In terms of coderivatives for vector-valued functions, we study perturbation analysis of error bounds for conic inequalities in the subsmooth setting. The main results of this paper are new even in the convex/smooth case.