A New Insight on Balanced Augmented Lagrangian Method

Motivated by the recent work [He-Yuan, Balanced Augmented Lagrangian Method for Convex Programming, arXiv: 2108.08554v1, 19 Aug 2021], a novel Augmented Lagrangian Method (ALM) has been proposed for solving a family of convex optimization problem subject to equality or inequality constraint. This new method is also extended to solve the multi-block convex optimization problem. Preliminary and some new convergence results are established with the aid of variational analysis for the saddle point of the problem and the first-order optimality conditions of involved subproblems.