Approximate Rolle's theorems for the proximal subgradient and the generalized gradient

Abstract

We establish approximate Rolle's theorems for the proximal subgradient and for the generalized gradient. We also show that an exact Rolle's theorem for the generalized gradient is completely false in all infinite-dimensional Banach spaces (even when they do not possess smooth bump functions). © 2003 Elsevier Inc. All rights reserved.