Regularization of proximal point algorithms in Hadamard manifolds

In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.