Higher-order metric subregularity and its applications

This paper is devoted to the study of metric subregularity and strong subregularity of any positive order for set-valued mappings in finite and infinite dimensions. While these notions have been studied and applied earlier for and-to a much lesser extent-for , no results are available for the case . We derive characterizations of these notions for subgradient mappings, develop their sensitivity analysis under small perturbations, and provide applications to the convergence rate of Newton-type methods for solving generalized equations.