TY - JOUR
T1 - Study on the Splitting Methods  for  Separable Convex Optimization  in a Unified Algorithmic Framework
AU - He , Bingsheng
JO - Analysis in Theory and Applications
VL - 3
SP - 262
EP - 282
PY - 2020
DA - 2020/09
SN - 36
DO - http://doi.org/10.4208/ata.OA-SU13
UR - https://global-sci.org/intro/article_detail/ata/18286.html
KW - Convex programming, augmented Lagrangian method, multi-block separable model, Jacobian splitting, unified algorithmic framework.
AB - <p style="text-align: justify;">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 solution 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 particular, exploiting this framework, we are able to give a very clear and elementary proof of the convergence of these solution methods.</p>