Hölder weak sharp minimizers and Hölder tilt-stability

Abstract

In this paper, we introduce and study the notions of Hölder weak sharp minimizers, stable Hölder weak sharp minimizers and Hölder tilt-stable weak minimizers for a proper lower semicontinuous function f on a Banach space. In terms of the Hölder metric subregularity/regularity of ∂f, we consider optimality conditions for Hölder weak sharp minimizers and stable Hölder weak sharp minimizers. We prove that x̄ is a stable Hölder weak sharp minimizer (resp. a Hölder tilt-stable weak minimizer) of f if and only if it is a stable Hölder sharp minimizer (resp. a Hölder tilt-stable minimizer) of f.