A nonsmooth Robinson’s inverse function theorem in Banach spaces

Abstract

In a recent paper, Izmailov (Math Program Ser A 147:581–590, 2014) derived an extension of Robinson’s implicit function theorem for nonsmooth generalized equations in finite dimensions, which reduces to Clarke’s inverse function theorem when the generalized equation is just an equation. Páles (J Math Anal Appl 209:202–220, 1997) gave earlier a generalization of Clarke’s inverse function theorem to Banach spaces by employing Ioffe’s strict pre-derivative. In this paper we generalize both theorems of Izmailov and Páles to nonsmooth generalized equations in Banach spaces.