  In this paper we present an inexact proximal point method for variational
inequality problem on Hadamard manifolds and study its convergence properties.
The proposed algorithm is inexact in two sense. First, each proximal subproblem
is approximated by using the enlargement of the vector field in consideration
and then the next iterated is obtained by solving this subproblem allowing a
suitable error tolerance. As an application, we obtain an inexact proximal
point method for constrained optimization problems, equilibrium problems and
nonlinear optimization problems on Hadamard manifolds.
