Proximal Point Methods with Bregman Function on Riemannian Manifolds

We study the proximal point algorithm with Bregman type distance to minimize the problem , , . ) ( min S x to s x f ∈ where S is an open convex subset of a complete simply connected Riemannian manifold M of non positive sectional curvature and f is a convex function in this manifold. Introducing a strong assumption on the geodesic triangle on this manifold we obtain the convergence of the sequences to a solution of the problem. Also we give some examples in the non-Euclidean case.