Reviews: Non-Ergodic Alternating Proximal Augmented Lagrangian Algorithms with Optimal Rates

Summary: The paper proposed 4 new variants of Augmented Lagrangian methods, which called NAPALA (non-ergodic alternating proximal augmented Lagrangian algorithms) to solve non-smooth constrained convex optimization problems under different problem structure assumptions. The first algorithm only requires f and g to be convex but neither necessarily strongly convex nor smooth. Especially, its parallel variant (8) has more advantages. The second algorithm requires either f or g to be strongly convex. Its variant (12) also allows to have parallel steps.