  In this paper, we consider the monotone generalized variational inequality
(MGVI) where the monotone operator is Lipschitz continuous. Inspired by the
extragradient method and the projection contraction algorithms for monotone
variational inequality (MVI), we propose a class of PGA-based
Predictor-Corrector algorithms for MGVI. A significant characteristic of our
algorithms for separable multi-blocks convex optimization problems is that they
can be well adapted for parallel computation. Numerical simulations about
different models for sparsity recovery show the wide applicability and
effectiveness of our proposed methods.
