A fast augmented Lagrangian framework and its application

Abstract

This letter investigates a fast augmented Lagrangian framework applicable to constrained convex optimization problems. By integrating the Aitken acceleration technique and the multi-direction acceleration technique, this framework enhances the convergence rate of the traditional augmented Lagrangian method and adapts to different types of constrained convex optimization problems on a case-by-case basis: (1) for problems with analytical solutions, the Aitken method is more suitable; (2) for problems without analytical solutions, the multi-direction method serves as a viable alternative. Furthermore, the proposed fast augmented acceleration technique is extended to system identification and the Alternating Direction Method of Multipliers (ADMM). The effectiveness of the framework is validated through convergence analysis and numerical experiments.