  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.
