On Lipschitz-like property for polyhedral moving sets

Abstract

We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on Relaxed Constant Rank Constraint Qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this aim we prove the R-regularity of the considered set-valued mapping and correct the respective proof given by these authors.