Covering on a Convex Set in the Absence of Robinson's Regularity
Aram Vladimirovich Arutyunov, Alexey F. Izmailov · SIAM Journal on Optimization · 2020
We study stability properties of a given solution of a constrained equation, where the constraint has the form of the inclusion into an arbitrary closed convex set. We are mostly interested in those cases when Robinson's regularity condition does not hold, and we obtain weaker conditions ensuring stability of a given solution subject to wide classes of perturbations, or, in other words, ensuring covering of a “large" set. Unlike previous developments of this kind, here we do not employ any necessary conicity assumptions on the constraint set, thus allowing for a much wider area of potential applications.