Dual conditions for error bounds of conic inequality in Asplund spaces

In this paper, we study error bounds for the conic inequality defined by a vector-valued function between Asplund spaces and a nonempty closed convex cone. We consider Fréchet/Mordukhovich subdifferentials of such vector-valued function with respect to the given closed convex cone and establish several dual necessary conditions for error bounds in terms of these subdifferentials of the concerned vector-valued function at points in the solution set. Furthermore, we investigate the composite-convex inequality defined by the composition of a smooth mapping with a cone-convex vector-valued function, and prove that the aforementioned dual conditions are also sufficient for error bounds.