Dini derivative and a characterization for Lipschitz and convex functions on Riemannian manifolds

Abstract

Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given.

Generalized gradients and characterization of epi-Lipschitz sets in Riemannian manifolds

“…Let us present two important examples of locally Lipschitz functions that arise naturally on Riemannian manifolds; see also [20]. ⟨U, V ⟩ = tr(UV ).…”

Necessary and Sufficient Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds

“…It is known that a convex environment has good properties for the search of optimal points. In Ferreira [13], the author gives necessary and sufficient conditions for convex functions on Hadamard manifolds. A significant generalization of the convex functions are the invex functions, introduced by Hanson [14], where the x-y vector is replaced by any function η(x, y).…”