A dual-primal balanced augmented Lagrangian method for linearly constrained convex programming

Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its subproblems and improving its implementation. In this short note, we propose a dual-primal version of the balanced ALM, which updates the new iterate via a conversely dual-primal iterative order formally. The proposed method inherits all advantages of the prototype balanced ALM, and its convergence analysis can be well conducted in the context of variational inequalities. In addition, its numerical efficiency is demonstrated by the basis pursuit problem.