Weak Sharp Minima and Finite Termination of the Proximal Point Method   for Convex Functions on Hadamard Manifolds
  In this paper we proved that the sequence generated by the proximal point method, associated to a unconstrained optimization problem in the Riemannian context, has finite termination when the objective function has a weak sharp minima on the solution set of the problem. 
G. C. Bento and J. X. da Cruz Neto
math.NA