A New Hybrid Generalized Proximal Point Algorithm for Variational Inequality Problems

Abstract

In this paper, we propose a modified Bregman-function-based proximal point algorithm for solving variational inequality problems. The algorithm adopts a similar constructive approximate criterion as the one developed by Solodov and Svaiter (Set Valued Analysis 7 (1999) 323) for solving the classical proximal subproblems. Under some suitable conditions, we can get an approximate solution satisfying the accuracy criterion via a single Newton-type step. We obtain the Fejer monotonicity to solutions of VIP for paramonotone operators. Some preliminary computational results are also reported to illustrate the method.