A New Penalty Dual-Primal Augmented Lagrangian Method and Its Extensions

In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the new iterates in a dual-primal order, and then be extended to solve multiple-block separable convex programming problems with splitting version and partial splitting version. We establish the convergence analysis for all the introduced algorithm in the lens of variational analysis. Numerical results on the basic pursuit problem and the lasso model are presented to illustrate the efficiency of the proposed method.