A New Penalty Dual-primal Augmented Lagrangian Method and its Extensions

In this paper, we propose a penalty dual-primal balanced-based augmented Lagrangian method for solving linearly constrained convex minimization problems. Convergence and convergence rate of the penalty dual-primal balanced-based augmented Lagrangian method are established by the tool of variational inequality. Further, we generalize the penalty dual-primal balanced-based augmented Lagrangian method to solve linearly constrained multi-block separable convex minimization problems with full splitting technique and partial splitting technique. Numerical results on the basic pursuit problem and the Lasso model are presented to illustrate the efficiency of the proposed methods.