Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 26 (2019), No. 4, 1059--1070Copyright Heldermann Verlag 2019 Gradients on Sets Jan Mankau Fakultät Mathematik, Technische Universität, 01062 Dresden, Germany jan.mankau@tu-dresden.de Friedemann Schuricht Fakultät Mathematik, Technische Universität, 01062 Dresden, Germany friedemann.schuricht@tu-dresden.de [Abstract-pdf] For a locally Lipschitz continuous function $f\colon X\to\mathbb{R}$ the generalized gradient $\partial f(x)$ of Clarke is used to develop some (set-valued) gradient on a set $A\subset X$. Existence, uniqueness and some approximation are considered for optimal descent directions on set $A$. The results serve as basis for nonsmooth numerical descent algorithms that can be found in subsequent papers. Keywords: Generalized gradient, set-valued gradient, generalized directional derivative, Lipschitz continuous function, optimal descent direction. MSC: 46T20, 47H04, 49K99, 65K10. [ Fulltext-pdf  (115  KB)] for subscribers only.