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In this paper an inexact proximal point method for variational inequalitiesin Hadamard manifolds is introduced and studied its convergence properties. Themain tool used for presenting the method is the concept of enlargement ofmonotone vector fields, which generalizes the concept of enlargement ofmonotone operators from the linear setting to the Riemannian context. As anapplication, an inexact proximal point method for constrained optimizationproblems is obtained.

Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds