Optimality conditions of first order for global minima of locally Lipschitz functions

Abstract

We show how the necessary conditions for a local minimum can be used to obtain a sufficient optimality condition of first order for a global minimum of a locally Lipschitz function on a closed convex set. Using a theorem of Clarke, we obtain a short proof and an extension to Banach spaces of a result of Hiriart-Urruty and Ledyaev.