A nonlinear proximal point algorithm

Exact and approximate versions of a nonlinear proximal point algorithm (NPA) are presented. Both are globally weakly convergent to a zero of T, a maximal monotone map on a real Hilbert space. Conditions implying sublinear, linear, superlinear, and finite convergence to the zero set of T are given. An implementation of the approximate version for T strongly monotone is stated. When applied to a convex (resp. saddle) function, the speed of approach to the minimum (resp. saddle) value is estimated.