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This paper presents a class of proximal point algorithms using a nonlinear proximal term for monotonic variational inequality problems. This work extents proximal point algorithms using Bregman distance for minimization problems, and differs with J. Eckstein's approximate iterations in Bregman-function-based proximal algorithms (1998). We study the convergence of the proposed algorithms  and obtain a $O(1/N)$ computing complexity/convergence rate of the algorithms. Further more, connections to some existed popular methods were given, which shows that our algorithm can include these methods within a general form.

On the Convergence and O(1/N) Complexity of a Class of Nonlinear Proximal Point Algorithms for Monotonic Variational Inequalities