Local Convergence of the Proximal Point Method for a Special Class of   Nonconvex Functions on Hadamard Manifolds
  Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained. 
G. C. Bento, O. P. Ferreira, P. R. Oliveira