On contractibility of the operator $I-t\nabla f$

Abstract

We study the set $K(f)$ of positive numbers $t$ for which the operator $I-t\nabla f$ is contractible, where $f$ is a differentiable function defined on a convex subset of the Hilbert space ($I$ is the identity operator of that Hilbert space). The set $K(f)$ is interesting for a problem of minimization of strongly convex functions when the method of contractible mappings is applied.