Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems

In this paper, we mainly study error bounds for a single convex inequality and semi-infinite constraint systems, give characterizations of stability via directional derivatives. For inequality, it is proved that the local under small perturbations essentially equivalent to non-zero minimum derivative at reference point over unit sphere, global be strictly positive infimum derivatives, all points in boundary solution set, sphere as well some mild qualification. When these results are applied also provided. particular such only require component functions systems have same linear perturbation. Our work demonstrates verifying is, degree, solving minimization problems (defined by derivatives) sphere.