Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework

It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality.Recently,we have proposed a unified algorithmic framework which can guide us to construct the solu-tion methods for solving these monotone variational inequalities.In this work,we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago.In partic-ular,exploiting this framework,we are able to give a very clear and elementary proof of the convergence of these solution methods.