Gap functions and globally projected differential inclusions on Riemannian manifolds

Abstract

We consider variational inequality problems on complete Riemannian manifolds and we introduce the globally projected differential inclusions associated with these problems. Then we show that every solution of a variational inequality problem is an equilibrium point of the associated globally projected differential inclusion. Finally, we prove that on a complete Riemannian manifold with nonpositive curvature, one can find a gap function for the variational inequality problem.