Variational Inequalities for Set-Valued Vector Fields on Riemannian Manifolds: Convexity of the Solution Set and the Proximal Point Algorithm

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds. The existence results of the solution, convexity of the solution set, and the convergence property of the proximal point algorithm for the variational inequality problems for set-valued mappings on Riemannian manifolds are established. Applications to convex optimization problems on Riemannian manifolds are provided.