Analysis on a superlinearly convergent augmented Lagrangian method

The augmented Lagrangian method is a classical method for solving constrained optimization. Recently, the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems. However, most Lagrangian methods use first order information to update the Lagrange multipliers, which lead to only linear convergence. In this paper, we study an update technique based on second order information and prove that superlinear convergence can be obtained. Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.