Implicit function theorem for nonsmooth systems by means of exhausters

Abstract

The implicit function theorem for nonsmooth systems is formulated by means of new tools of nonsmooth analysis — exhausters. Exhausters exist for any directionally differentiable function whose directional derivatives are directionally continuous functions. It is possible to find an implicit function with the help of exhausters for functions that are not Lipschitz and not quasidifferentiable but directionally differentiable. Examples of calculating nonsmooth implicit functions are given.